I have handled problem (coincidentally, also in 3.5) from both sides of the DM screen.

Encourage characters that don't "play out"

The reason characters get abandoned is that the player is not interested in that character's growth anymore. It's important to note that growth can come from either mechanics or roleplaying, and either one can keep a character in the game.

Roleplaying growth

This one is fairly simple. "John Smith, mercenary who fights for gold" with 14 Fighter levels is a stillborn character. Encourage your players to create characters with meaningful desires, goals, and values. Maybe John Smith yearns to pass the wizarding college exam, or has a rival he wants to put in his place, or is trying to win the affection of a handsome red dragon. There is now a new dimension to this character that the player can explore in roleplay. It helps if you play in a well-detailed setting, because then John Smith's player can make choices motivated by his goals, such as "let us travel to the ancient Illefarn Empire and dig for scrolls so I can impress the Wizard College, and I guess you guys can find sweet loot."

Without relying on players to provide these conflicts, you can provide them yourself. A particularly nasty NPC opponent that taunts and dupes the party and then runs away can be effective here - he has wronged these specific characters, and their players won't rest until they've put him in the ground!

Mechanical growth

A lot of character builds in a lot of systems simply don't scale well. They are effective within a range of levels - before those levels they are unattainable, and after they are useless. Players who end up with such a character would be motivated to ditch them once their usefulness is at an end. As a D&D 3.5 example, compare the druid, cleric, and paladin. The druid gets cool stuff all through his career, the cleric stops getting class features after level 1 but still gets spells, and the paladin gets extra weekly uses of a 3rd level spell and practically nothing else after 5th level. The paladin's player would be very tempted to roll a new character as soon as his abilities stopped getting better.

To combat this, players can select character classes that are effective at all levels, but this requires a degree of system mastery. The DM can entice players of poorly scaling characters with quests and rewards tailored to them - being a paladin can suddenly get good with the appearance of a Holy Avenger sword, or the character's induction into the Knights of the Raven, opening up a powerful prestige class.

Allow retraining/rebuilding

If a player is happy with his character concept, but it turns out he's having trouble contributing to the game because of low skills, he can be tempted to ditch the character and make a new, effective one. You can work with the player to tweak his character build without getting rid of the concept, so there is some continuity to the storyline despite under-the-hood changes.

Ah I know the feeling. Many people have this condition. I think it's mostly due to the fact that creating a new character is simply a lot of fun. All possibilities are open and you can think of so many new ways to go about making the new you!

A way to combat this is to ask your players, when they create a new character, to not just think about their characters' history up until now, but also their future. As in, what do their characters want to achieve in the world? What are their goals? I mean this in a role play way, not just 'I want to become a level 20 wizard' or 'I want to defeat monsters and collect gold'. Pretty much no-one is that one-dimensional.

After they have though of some goals, it is your job as GM to incorporate these in the campaign, so that they become a real thing instead of just another story on a piece of paper. I have played a pirate campaign where my backstory was that I was a bastard son of a noble family that was outcast. My long term goal was to avenge my mother, who they had murdered, and show my family that I was worth something after all (in a nutshell). So the GM made sure that I'd pick up leads about what my family members were up to on our adventures, and every now and then I'd encounter one of them which could lead to a small side quest for me to do alongside the main mission for the group (or it could lead to me murdering them). I ended up being a pirate captain and raiding their castle, which was mightily satisfying. The other characters had been beside me for a while, had seen my struggles with the family and were more than happy to go along on my crusade for vengeance. It became a second campaign inside the main one, all pretty organically.

The GM did this for all players and it really gives the characters more flavor and a reason to keep playing them. It doesn't have to be that hard to incorporate. A town mayor that gave the party a quest simply became a town mayor who also happened to be one of my nephews. Just make sure that you keep it small (at least at first) so that the campain doesnt become 'everyone doing their own thing'.

The other answers here are quite good, I just wanted to add a couple specific techniques that I have found useful in my gaming groups.

Character Back Stories

I had a GM who required that each player write a 1 page back story (you can of course lessen this requirement as you see fit) for their characters that they would send him before they were allowed to join the campaign. This had three major effects.

1. It made the players feel invested in the character: After spending a while writing about a character it is impossible to not feel a connection to them
2. It gave the GM ideas of things to add to the campaign as side quests: For example one character was a monster hunter whose family was killed by a werewolf raid, so we ended up on a quest to kill the leader of the werewolves.
3. It established a basis for RP for the rest of the campaign: Once you give a character a personality and back story it is really easy to think of what that character would do in a given situation.

Also useful would be to at least come up with a list of things they have to fill in before they can play. For example: hometown, age, adversaries, friends, family, how they became the class they are, a traumatic event in their lives, etc. I do this for all of my characters now just because it makes my characters more rich and interesting, which makes me enjoy playing them a lot more.

Come Up With Short and Long Term Goals

In my current group we come up with both short and long term goals.

The short term goals are things that can be done in a session or two, and we sometimes come up with multiples of these at once. Things like "Land the killing blow on an enemy", "Make a new (npc) friend", and "Recruit someone into my religious sect" have all come up as short term goals. These makes the players pay closer attention to the game and makes them investigate situations more than they would normally because they are looking for ways to fulfill their short term goals.

Long term goals are things that give each character a deeper motivation. These are things that are going to be resolved on the scale of a whole campaign or even longer. Things like, "Become the leader of my monastic order", "Rebuild my town that was destroyed by raiders", "Avenge my murdered family", and even "Become a deity" have been long term goals in my group, which have all lead to really interesting character growth and side quests.

The GM can then either reward characters that fulfill these goals, or at least provide opportunities for completing them, and let the satisfaction of checking them off your goal list be its own reward.

I'll come at this from another angle.

Sometimes the players themselves have a hard time creating a character of any real substance. I, for one, am really bad at this. My two favourite characters are:

• Torbinn Norfall: A blue Dragonborn Fighter, with a hidden past that he is ashamed of.
• Sam Durey: A Garbage truck driver, who spends all his time on the job, or at the pub.

Not exactly what you would call "rich" characters. However, as the story(s) developed, these characters created their own identities through the adventures they had travelled on, with a fair amount of input from the GM. Now;

• Tobrinn was a Commander of the Dragonborn Cavalry, whom due to poor judgment, led his men to their deaths by drowning in a swamp in an attempt to flank the enemy. He was unknowingly possessed by the souls of his fallen men, cursed by his betrayal of their trust. In an attempt to regain redemption, (all but one) of the souls were extracted, but we abused by the evil power of the sorcerer that nearly killed Tobrinn. He now searches for a hope to regain his honor, and lay the soul of his second-in-command to rest.
• Sam was a simple man. He had no goals or ambitions. He didn't really live life, he just trudged through it - day by day. Until the sky went dark. Now, he fights for his survival, and to protect the only friends he has ever had - a rag-tag bunch of misfits just trying to stay alive for another day; and he will do whatever he can to keep them safe.

Now that's muito Melhor.

In this way, with a little prompting and a little more effort on the behalf of the GM, I got pretty damn upset when I nearly lost either of these characters. So something to try is to create situations that draw in the player.

Algumas coisas para tentar:

• Before a game, talk to the group, and get into a conversation about each of their favourite characters. What were they like? What was their favourite experience with those characters? Take note of this, and try and create similar experiences.
• Create situations for the jogador, não o personagem. How would the player react in certain situations?
• Create them for each Individual player, rather than just the group. Make them feel special, like this side-quest is their main focus (Maybe the Guildmaster has a job just for the Rogue, or someone needs a body guard, and the tank look like they'll do a great job). This may get a little boring for the rest of the players in the meantime, they're still involved, but the focus is on one player (and their character) at a time.

Hopefully then the players will start to feel a little more invested in their characters (You can test this by giving them "soft deaths" - a cliffhanger ending that leaves the group to an unknown fate, like a pitfall that poder leave someone dead - only to have everyone ok in the next session). Check their reactions, and if they're concerned about this, then you're on the right track.

Heads-up: this post is a bit of a wall of text. I've italicized key bits to help with the length.

Finally, a Question About Me

I'm one of those players who winds up with a new character every session, unless the system's just too complex to do that with. I never am happy with the mechanics of a build (even though I've got good optimization skills and never wind up with an incompetent character), so I've got a bit of perspective as I go in here. I mean, heck, I ran through six characters (each with full builds, none of whom died) over the course of a month and a half and três sessions in the most recent game I've been playing in (mercifully for the GM, most of the changes happened in the gap between sessions, and he knew not to trust anything that wasn't pushed at him on the day of the game).

The reasons I've abandoned characters are two-fold: I either fall out of love with the character's concept, or I feel that they can't have the impact I want them to have in the story.

Some of this comes from my own fault: for instance, I make a murderhobo in a campaign that really requires more politics and subtlety, and not every player can have a character that's perfect for sticking around. Alternatively, I create a character and don't feel I can roleplay them in the way I want to play them, either because they don't fit the setting or my personality. You can easily mitigate these factors, though a player who is a persistent character jumper may simply need to ease out of it with discipline and practice:

Working the Character into the Story

So when you have a player who jumps characters, take a look at what they're submitting for their character sheets. I typically write about a page of backstory notes for my characters, and if that backstory doesn't come up it reduces my satisfaction with that character.

As a GM, if I see someone who writes a backstory but still consistently changes character, that indicates to me that they are unhappy with the way their character is fitting into the story.

As a GM, I try to work at least one element from each character's backstory into a game (at least if I have a written backstory). I don't have any persistent character hoppers, though my brother and I both hop characters a lot. I think that this works well, and it's also a great way to encourage players to actually put some thought into their characters.

Now, there are really two sub-sets of working a character into the story. I like to make memorable characters that people enjoy (social-driven characters), but there is also the element of changing the story (narrative result-driven characters).

Hooking Players who Want Memorable Characters

When a player who makes characters that generally succeed at their agenda [note that this is perception and result, not probability, based], and have a backstory, keeps hopping between characters, I find that the best result comes from linking their characters into the story to reward social-driven characters.

At the very least, I like to see at least one of the following mentioned by my GM when I play each game:

• Hometown/culture/civilization
• Training/source of power
• Old friends/enemies

This lets me know that my character is engaging for others, or at least the GM. Now, some of this is a little bit of extra work for the GM, but I've been known to leak my character backgrounds to other PC's to get a bit of an edge on that, and use their feedback and design to tweak the character.

Now, there are balance concerns with some bits of integrating a backstory in this way. In the first game I GM'ed, I allowed a player to introduce an NPC without vetting it: a Shadowrunner's "black market contact" became an "underworld crime boss", but if you are cautious this won't be an issue.

Giving the Character an Opportunity to Change Things

When I get characters who have the backstory and are ineffective and get swapped out a lot, I worry about providing agency for narrative result-driven players.

I typically handle this in one of two ways:

Managing Inefficiency

The first concern I look at is whether or not a character just fails to deliver on its premise. Often new roleplayers or roleplayers new to a system will want a character to do something they don't really do.

There are a couple of ways to deal with this, and I'll list them in the order I'd attempt to fix them:

First, try some mechanical tweaks that move the character to a spot within the player's desired archetype/result set. Sadly, this isn't always possible, either because it doesn't fit the setting or the mechanics, or because the player is stuborn.

Second, give the character more opportunities to shine at what they do well. Rarely will a character abjectly fail at everything, so you can toss a few nice and easy rolls at the character to increase their perceived effectiveness and put more of the narrative spotlight on them.

Third, work on a new character together with the player. This is a last resort, because it can perpetuate the problem. Make it clear that you don't want the player switching characters as often as they do, and that you are cooperating to find them a forever character that is compelling to them and matches the mechanical needs of a good character in your game.

Managing Agency

Sometimes, players just want power and they're not getting it. After all, roleplaying is a storytelling experience, and some people want to drive the storytelling. As a GM, you likely have one central narrative that you are working on, and that's okay (in fact, it's probably good, as you can put more effort into the high-octane fireworks shows that everyone gets to enjoy), but you can also provide smaller character-centered narratives that give the player more of what they want.

Some of this comes from heavily GM driven games; for instance, I'm in a D&D game that leaves me borderline satisfied; my character is compelling to me, but not particularly effective, being a Druid with a focus on healing and utility spellcasting. This means that I don't really get a whole lot of individual input: my character isn't built to solo dungeons, nor can I really veto the party's actions if they move the main thread in a way I disagree with as a player (roleplaying or otherwise).

The problem that I have that makes me constantly want to switch characters in that game is that I don't have good agency; my character doesn't have any thread to pursue, and doesn't engage well with the main thread of the game.

Unfortunately, as a player, even if someone wants to create a character to engage with the central story it can be difficult to create a character that really has much control over the main plot. Giving them a dedicated thread will allow you to give them a personalized and tailored experience that tells them that their character can change the world to fit their needs. Work in that backstory and give them a plot arc for their character.

Dealing with Other Character Hoppers

If a player isn't giving you a backstory for their characters, talk to them and make sure they aren't just being coy/not bringing it up. If they don't really care that much about the story, and they're switching characters because of mechanical reasons, you want to look more at helping them be satisfied with what they've got.

Reconstruindo

You can allow a character to retrain, giving players an opportunity to tweak or alter their characters. Typically, I've allowed most new players to make wholesale edits to a character so long as they don't change their general archetype (and I allow some stretches). Limiting them slightly but giving them the flexibility to change keeps you from having to deal with entirely different characters showing up each week.

Note that this can be a balance concern: if a veteran player can't make a character that fits their minimum power level for satisfaction, I don't let them keep tweaking until they have reached peak efficiency. At some point, put your foot down.

Use a Carrot...

One thing I do in a lot of my games is to incentivize characters being around a long time by giving them bonuses such as gear or special abilities that will not transfer to a new character. This satisfies powergamers, and also lets me better balance character power levels (most of my group are either powergamers or power-focused narrative gamers), and it leaves each member of the group at more or less the same power level if a character dies or a new player joins the game.

...or Use a Stick

If the habit is disruptive and prolonged, talk with your player and tell them that it's not acceptable, though you are willing to take steps to mediate it. If you can come to a conclusion on a way to resolve the character switching issue, you've already succeeded. Make sure to clearly communicate that their character switching is causing issues for you as a GM, who has to plan around new characters each week, and for the players, who are missing out on the story that can develop around a core set of characters.

If not, you need to start looking at more drastic methods.

First, you could make all characters start from square one in character development. As someone who has always had a thing for low power level campaigns, I like this concept, but it does mean that you will have an unbalanced party. You can also start characters out with a bit of developmental lag (in my Degenesis campaign, for instance, I tracked separate "survival XP" and "roleplaying XP" counts, and only the survival XP was given to new characters).

Second, you can just force the player to play a single character. If they adamantly refuse, you can give them a quota for how often they can switch characters. Ideally, once they've spent some time with a character they will click (even if it takes a few sessions and a couple characters) and continue playing that character.

Finally, if it gets to be such a problem that you and your players are all concerned, you can remove the problem player from the game. This is the nuclear option, and it's the very last thing here for a reason. Make your reasoning clear and communicate your expectations. You don't have to ban the player for life, but you do need to make it clear that you will make decisions that reinforce the good of the whole group, rather than the whims of an individual.

Role-playing for Role-playing's sake

Other answers here sort of start on the assumption that something is wrong with your group, that they don't grow more attached to their characters. I’ll give this group the benefit of the doubt and suggest your players may simply enjoy experimenting creating and role-playing different characters.

You mentioned playing several campaigns over the past few years. So if your players stuck with the same character through a campaign, they would have played only a handful of characters in that time. For some folks, that's not a lot of variety.

NOTA: These are all ideas to run by your players. When you do, ask if you can get a commitment not to abandon their characters in your main campaign, for the good of the story.

Variety Nights

Instead of rotating characters through the same campaign, you can just switch campaigns for a session or two. Run a group through a module like The Lost Mines of Phandelver (or other reasonably short adventure) and then call it quits for that party.

Since your players like variety so much, you might try mixing up games too with different setting. I won't recommend a game here, but you might look for one where character generation is quick, and you could make characters and run through an adventure in a session or two.

And if this sounds like a lot of work, yes it is. Share the load if you can by switching off who GM’s.

Loosen up retraining rules

You mentioned your players are power gamers. If they're interested in optimizing their characters, they may feel constrained by the 5e rules, and get frustrated they aren’t able to fix (perceived) mistakes in their character builds. So, let them modify their characters, and encourage it as an alternative to abaondoning them.

Crazy Ideas from where Chaos Reigns

You can even allow for massive changes to the characters. If a character really wants to switch from Elven Barbarian to Dwarven Bard, you can let their wish be granted by a god, or by having their body switched with someone else’s by an insane wizard.

Getting back to the story

This will certainly slow things down for the “main” campaign. You’ll need to shorten up your campaign and make it really focused (limit side quests and random encounters) if you want your players to remember the details from one session to the next. But I suspect when your group decides to play the main story arc, they will be more content to play “the same old boring characters.”

You need to create character attachment for the players. If a player is ditching their characters all the time, it is unlikely that they are very attached to any of them. As other posts have mentioned, you can do this best through role play via back stories and goals. Those are specific items though, not so much a technique.

Creating back stories and goals are just two methods of a technique I call "putting down roots". (Or, if I'm doing it as a player without the DM's help, "digging in".) Putting down roots is all about getting the character as tied up in the story and world as much as possible in a way that holds the interest of the player. You'll need to start with world and story elements the players like, so it's best to talk to them first and cater to their tastes. Roots come in many forms.

• Contacts. Friends, family, and loved ones in the form of NPCs. It is best if at least some of these characters are helpful to the PC in some way, so they have a reason to care about them. Love is reciprocal. This gives them people, (and, by extension, places) to actively care about in the here and now. They are also powerful literary tools, not just as plot devices mind you, but as social catalysts for role play. Do not use a character's contacts solely as a new way to torment them, it will make the player hate those NPCs, as they are a living weakness under such activity.

• Property. A lot of games do not even consider ownership of major property, (land, a business, a vehicle, etc.) or if they do, it is seen as a balance threat and made outlandishly expensive. It is OK for a PC to have a home, even if it doesn't belong to them. It could be the mages college they were trained in, or the sewers they grew up in as an orphan, or the ruins of their parents house. Whatever it is, tying the PCs to an actual physical place gives them some context for their place in the setting. Suddenly, a journey to another continent becomes a point of major concern- that is a LONG way away from home. It also gives then a reason to come home. Again, this ties them to the here and now.

• With background stories, help the players write their characters into the history of the setting itself, don't let them be an abstract entity who came from nothing, or whose glorious past exists in a vacuum. Even so much as a specific birth date is beneficial. Any original elements of their back story should be incorporated into your setting, at least in point-form notes, just in case the players decide to take a trip down memory lane. Any old mentors, friends, enemies, lovers, homes, heirlooms, etc. should still be out there in the world somewhere. There should be records, proof of their existence, a finger print or foot print left in the world in their wake.

• With goals, you need to have at least 3 of them, at least one must be a short-term goal, and the remaining two should be long-term goals, with the third being a target in the far future of the character's life. Each goal must be tangible, (something that can be identified in a clear, objective way. "Enlightenment", for example, is intangible.) and attainable, meaning the PC must actually be capable of succeeding. That doesn't mean they should always be successful in every goal, but the possibility should be there. Every time a goal is completed, or becomes significantly closer in time, its space must be filled by a new goal. This keeps the PCs always moving forward, not just whittling their way toward a specific target. Finally, and this is important, every goal must be important in some way to the whole PC, both the player and the character should have motivation. I learned these goal-setting methods from self-help books aimed at people with suicidal tendencies. If it can make someone want to keep living, it can make someone want to keep playing. In order for all of the above to work, whenever a player accomplishes a goal, it MUST impact the setting. It must make a meaningful and lasting change in the world, not just their paperwork.

All of these roots are just another way for a player to take hold of the world and shape it- to own a little piece of the setting, the story you are sharing with them. It turns their character into a gift box filled with sentiment, and a tool box filled with inspiration.

Another technique is building player-character identification. The way I think about this is based on theories about theory of mind, empathy, and cartoon character design. The player, and you, need to know who your character is on a fundamental level in order to do this. Get them to write down 10 items in a list for each of the following items:

• what makes your character happy

• what makes your character angry

• what makes your character scared

• what traits in other people are appealing

• what traits in other people are appalling

With these lists as a guideline, players can begin to get a sense of their character as more than just a pile of numbers. Rather, they come to get to know the character as if they were a person. The DM can then latch on to this information and cater to the character in a way that allows the player to explore what it would be like to be that person. This is where identification comes in. By walking in that character's boots, the player gets to become another- that is the greatest power of an RPG after all! Note that the lists are all material. They say nothing about values, or morals, or hopes, or dreams, or any of that stuff. This allows a new character to still be a blank slate. It gives the player room to play and work- a soul-shaped hole in the character for the player to fill. The player can decide for themselves through play what that information means. Simply by giving the players more opportunities to explore their characters' preferences, you are allowing them to build their characters in the literary sense, not just a mechanical sense. If you allow those lists to grow, and shrink, and change over time, then you are also opening the door for true character growth and a chance for a PC to become a real dynamic character, if that exploration ultimately changes their values.