The Ring is a Ring of power, and it increases the desire for power in those who wear it; this effect is amplified in direct proportion to the wearer's innate desire for power. This effect is a reflection of Sauron's own personality.
A Brief Biography of Sauron:
Sauron wasn't always evil. He began his life as a Maia, essentially an angel, and of the same class as Gandalf and the other wizards. He was eventually corrupted by Morgoth, and became his most powerful lieutenant, but he never really had the same motives as Morgoth. Morgoth was one of the Valar (demigods or Archangels), and was far more powerful than Sauron; in fact, Morgoth was the second most powerful entity in the universe after Eru Ilúvatar (who is basically analogous to the Judeo-Christian god). While Morgoth was still around, Sauron seems to have served him very faithfully, but after Morgoth's defeat and exile into the void, Sauron showed himself to be somewhat different from his former master.
From the very beginning, or nearly so, Morgoth's motives were purely destructive in nature: he wasn't trying to rule the universe so much as he was trying to destroy it altogether; he wasn't necessarily opposed to the idea of being a god unto the inhabitants of Arda, but his ultimate goal was to undo the creation. Sauron wasn't such a nihilist at heart. In fact, Sauron's initial motivation wasn't entirely malicious: he didn't want to destroy the world, or even rule it for his own sake; he saw suffering and chaos, and he believed he could impose a sense of order and harmony on the world, redirecting the harmful, negative impulses of humans, Elves, and Dwarves into constructive, positive purposes, thereby benefiting everyone involved. But he fell under the sway of Morgoth, and he followed his master's orders without question.
When Morgoth was finally overthrown, Sauron was summoned from Middle-earth to Aman, there to stand trial for his crimes against the Children of Ilúvatar and the creations of Eru, and to face the judgement of the Valar and Maiar, who are collectively known as the Ainur. Sauron seems to have repented, although this repentance may have been motivated more by fear than by genuine remorse. He struggled with his pride, but in the end, he couldn't bring himself to face the humiliation of being judged by his fellow Ainur. He fled to the east, and from that moment, he was beyond redemption.
He attempted to realize his ambitions - to impose order on the world and bring an end to the senseless destruction and chaos which plagued it, but, predictably, not everyone was willing to submit to the will of Morgoth's former lieutenant.
The Edain - the Men who became the Dúnedain, and who were the friends of the Elves - along with the Elves, resisted Sauron, and thwarted his attempts to subdue the world to his will. Sauron was outraged, and so began his desire to rule the world for his own benefit, rather than the benefit of all. He resolved to seize power by any means necessary, and to kill all who stood in his way. It was in this spirit that he made the Ring, and the Ring was a reflection of his will.
It is unlikely that Sauron deliberately made the Ring in such a way that the person who bore it would be pathologically possessive of it: this would only be possible if Sauron had anticipated that he might lose the Ring - something that would require that he was defeated in battle. If he was capable of predicting such a thing, I don't think he would have made the Ring in the first place. He obviously never imagined that anyone would try to destroy the Ring, which is exactly why it ended up being destroyed; I think he was similarly incapable of anticipating that he and the Ring would ever be separated. He thought he was invincible. He couldn't have imagined that the Ring would ever be anywhere but on his finger, and if he did imagine it, he wouldn't have made the Ring at all.
The Nature of the Ring
Now Sauron's lust [for power] and pride increased, until he knew no bounds, and he desired to make himself master of all things in Middle-earth... He brooked no freedom nor any rivalry, and he named himself Lord of the Earth.
- The Silmarillion: Of the Rings of Power and the Third Age
And much of the strength and will of Sauron passed into that One Ring; for the power of the Elven-rings was very great, and that which should govern them must be a thing of surpassing potency...
- The Silmarillion: Of the Rings of Power and the Third Age
At the end of the War of the Last Alliance (between Men and Elves), Gil-galad and Elendil struck down Sauron, but were killed themselves in the process. Elendil's sword, Narsil, broke beneath him, but his son Isildur took the hilt shard and cut the ring finger from Sauron's hand. Sauron was cast out of his bodily form, and Isildur took the Ring; Elrond and Cirdan the Shipwright urged him to destroy it in the fires of Mount Doom. But even though Sauron was defeated for the time, the Ring's power still remained, and Isildur could not bring himself to destroy it. He claimed it as an heirloom and a wereguild for his father's death. Shortly afterwards, he was ambushed by a host of Orcs, and put the Ring on his finger to escape. While swimming across a nearby river, the Ring was lost:
There the Ring betrayed [Isildur] and avenged its maker, for it slipped from his finger as he swam, and it was lost in the water. Then the Orcs saw him as he laboured in the stream, and they shot him with many arrows, and that was his end.
- The Silmarillion: Of the Rings of Power and the Third Age
E:
[Sauron] only needs the One; for he made that Ring himself, it is his, and he let a great part of his own former power pass into it, so that he could rule all the others.
- Gandalf, The Fellowship of the Ring
E:
‘What do you mean?’ said Frodo. ‘Surely the Ring was [Gollum's] Precious and the only thing he cared for? But if he hated it, why didn’t he get rid of it, or go away and leave it?’
‘You ought to begin to understand, Frodo, after all you have heard,’ said Gandalf. ‘He hated it and loved it, as he hated and loved himself. He could not get rid of it. He had no will left in the matter.
‘A Ring of Power looks after itself, Frodo. It may slip off treacherously, but its keeper never abandons it. At most he plays with the idea of handing it on to someone else’s care – and that only at an early stage, when it first begins to grip. But as far as I know Bilbo alone in history has ever gone beyond playing, and really done it. He needed all my help, too. And even so he would never have just forsaken it, or cast it aside. It was not Gollum, Frodo, but the Ring itself that decided things. The Ring left him.’
-ibid
E:
‘There was more than one power at work, Frodo. The Ring was trying to get back to its master. It had slipped from Isildur’s hand and betrayed him; then when a chance came it caught poor Déagol, and he was murdered; and after that Gollum, and it had devoured him. It could make no further use of him: he was too small and mean; and as long as it stayed with him he would never leave his deep pool again. So now, when its master was awake once more and sending out his dark thought from Mirkwood, it abandoned Gollum. Only to be picked up by the most unlikely person imaginable: Bilbo from the Shire!
- ibid
But why was the lure of the Ring so strong?
Because it tailored its appeal to the specific person it was calling to.
Tolkien scholar Michael Martinez writes on his "Middle-earth & J.R.R Tolkien Blog":
The Ring appears to have cherry-picked whom it would tempt.
We can see this tailor made allure in each case in which the Ring tempts someone:
Gandalf is described, in O Silmarillion, as a disciple of a Vala named Nienna, who is essentially a goddess of pity, mercy, and sympathy; the Ring appeals to these attributes:
[Frodo says] ‘But I have so little of any of these things! You are wise and powerful. Will you not take the Ring?’
‘No!’ cried Gandalf, springing to his feet. ‘With that power I should have power too great and terrible. And over me the Ring would gain a power still greater and more deadly.’ His eyes flashed and his face was lit as by a fire within. ‘Do not tempt me! For I do not wish to become like the Dark Lord himself. Yet the way of the Ring to my heart is by pity, pity for weakness and the desire of strength to do good. Do not tempt me! I dare not take it, not even to keep it safe, unused. The wish to wield it would be too great, for my strength. I shall have such need of it. Great perils lie before me.’
- The Fellowship of the Ring
Galadriel, proud and beautiful, is tempted by visions of being even more beautiful and beloved:
`And now at last it comes. You will give me the Ring freely! In place of the Dark Lord you will set up a Queen. And I shall not be dark, but beautiful and terrible as the Morning and the Night! Fair as the Sea and the Sun and the Snow upon the Mountain! Dreadful as the Storm and the Lightning! Stronger than the foundations of the earth. All shall love me and despair!‘...
- The Two Towers
Faramir:
‘So it seems,’ said Faramir, slowly and very softly, with a strange smile. `So that is the answer to all the riddles! The One Ring that was thought to have perished from the world. And Boromir tried to take it by force? And you escaped? And ran all the way — to me! And here in the wild I have you: two halflings, and a host of men at my call, and the Ring of Rings. A pretty stroke of fortune! A chance for Faramir, Captain of Gondor, to show his quality! Ha!’ He stood up, very tall and stern, his grey eyes glinting.
Frodo and Sam sprang from their stools and set themselves side by side with their backs to the wall, fumbling for their sword-hilts. There was a silence. All the men in the cave stopped talking and looked towards them in wonder. But Faramir sat down again in his chair and began to laugh quietly, and then suddenly became grave again.
- ibid
Note: In my opinion (and Tolkien's - he said so in a letter, but I can't include it here because of space restrictions) Faramir is not particularly tempted by the Ring, and this is because he, unlike his brother Boromir, is humble. Boromir, by way of comparison, is vainglorious and proud, and seeks glory in battle. Faramir does not relish military triumph, and kills only with regret. In the scene in which Faramir resists the Ring, he actually commands Frodo não to show it to him, and says he wouldn't pick the Ring up if he saw it laying on the road.
The same idea - that humble people are less tempted, or rather, more able to resist the temptation, than are proud and vainglorious people - applies to Samwise; again we see the Ring tailoring its appeal to the individual (bear in mind that Sam is a gardener):
His thought turned to the Ring, but there was no comfort there, only dread and danger. No sooner had he come in sight of Mount Doom, burning far away, than he was aware of a change in his burden. As it drew near the great furnaces where, in the deeps of time, it had been shaped and forged, the Ring’s power grew, and it became more fell, untameable save by some mighty will. As Sam stood there, even though the Ring was not on him but hanging by its chain about his neck, he felt himself enlarged, as if he were robed in a huge distorted shadow of himself, a vast and ominous threat halted upon the walls of Mordor. He felt that he had from now on only two choices: to forbear the Ring, though it would torment him; or to claim it, and challenge the Power that sat in its dark hold beyond the valley of shadows. Already the Ring tempted him, gnawing at his will and reason. Wild fantasies arose in his mind; and he saw Samwise the Strong, Hero of the Age, striding with a flaming sword across the darkened land, and armies flocking to his call as he marched to the overthrow of Barad-dûr. And then all the clouds rolled away, and the white sun shone, and at his command the vale of Gorgoroth became a garden of flowers and trees and brought forth fruit. He had only to put on the Ring and claim it for his own, and all this could be.
- ibid
The Exception that Proves the Rule:
Now, to highlight the way the Ring works its influence on people, we will turn to the only character who is totally immune to it: Tom Bombadil. Martinez explains this in the blog post linked above. Here is the passage in which Bombadil and the Ring come face to face:
Indeed so much did Tom know, and so cunning was his questioning, that Frodo found himself telling him more about Bilbo and his own hopes and fears than he had told before even to Gandalf. Tom wagged his head up and down, and there was a glint in his eyes when he heard of the Riders.
‘Show me the precious Ring!’ he said suddenly in the midst of the story: and Frodo, to his own astonishment, drew out the chain from his pocket, and unfastening the Ring handed it at once to Tom.
It seemed to grow larger as it lay for a moment on his big brown-skinned hand. Then suddenly he put it to his eye and laughed. For a second the hobbits had a vision, both comical and alarming, of his bright blue eye gleaming through a circle of gold. Then Tom put the Ring round the end of his little finger and held it up to the candlelight. For a moment the hobbits noticed nothing strange about this. Then they gasped. There was no sign of Tom disappearing!
Tom laughed again, and then he spun the Ring in the air — and it vanished with a flash. Frodo gave a cry – and Tom leaned forward and handed it back to him with a smile.
- The Fellowship of the Ring
We see something astonishing here: This object, in which the fate of the entire world is bound, is powerless in Tom's hands. He thinks so little of it that he treats it like a toy, a mere trifle, of no importance or danger. How are we supposed to make sense of this? Martinez has a very plausible explanation, and again, it has to do with the Ring's modus operandi - appealing to the personality of the individual:
Given that Bombadil asked to see the Ring, and that he played with it and at one point had a gleam in his eye, I don’t see any justification for concluding that he was not tested by the Ring like others. Bombadil probably had the easiest test of all because he had already long before made his choice about mastery over others.
Bombadil allowed evil things to remain in his land — not because he wanted them there but because he did not want to destroy them. He probably set the boundaries of that land to keep those evil things from troubling Men and Hobbits (his neighbors).
Bombadil didn’t believe in creating prisons for the barrow-wights and... Old [Man] Willow; he just didn’t succumb to their evil ways. Hence, the Ring could have shown him a world where he roamed free and evil things didn’t bother him (and perhaps didn’t bother anyone else). Or the Ring could have shown him a world where he could “master” anyone and anything. The point is that the Ring definitely could have shown him something, even if it was more absurd and silly than what it showed to Sam.
And obviously, whatever the Ring showed Tom, he wasn't interested.
Tolkien explains why in Letter #144:
Tom Bombadil is not an important person – to the narrative. I suppose he has some importance as a 'comment'. I mean, I do not really write like that: he is just an invention, and he represents something that I feel important, though I would not be prepared to analyze the feeling precisely. I would not, however, have left him in, if he did not have some kind of function.
The story is cast in terms of a good side, and a bad side, beauty against ruthless ugliness, tyranny against kingship, moderated freedom with consent against compulsion that has long lost any object save mere power, and so on; but both sides in some degree, conservative or destructive, want a measure of control.
But if you have, as it were taken 'a vow of poverty', renounced control, and take your delight in things for themselves without reference to yourself, watching, observing, and to some extent knowing, then the question of the rights and wrongs of power and control might become utterly meaningless to you, and the means of power quite valueless. It is a natural pacifist view, which always arises in the mind when there is a war.
So the thing that makes the Ring so appealing to almost everyone else is the same thing that makes it powerless against Tom Bombadil. He has deliberately chosen to reject control over anything but himself. He himself is good, but he doesn't take sides in the battle between good and evil. He doesn't care about who wins or loses, because he has renounced power, control, and conflict. These concepts have no meaning to Tom. He is exclusively an observer, and his only interest is in things for their own sake. Tom doesn't approve of Old Man Willow's attempt to eat the hobbits, and he stops him from doing so, but he still respects Old Man Willow and his right to exist. The fact that Old Man Willow is probably evil, at least to some extent, doesn't enter into the equation.
The Ring is a device of power, and power is its only means of influencing and manipulating people. Tom Bombadil is diametrically opposed to power, and therefore, the Ring is powerless to corrupt or tempt him. It is interesting (and amusing) to imagine the Ring desperately trying to find a chink in Tom's armor, searching in vain for a way to reach him, and silently screaming with rage when he treats the Ring like a silly little toy. Because the Ring tailors its appeal to the individual's unique weaknesses (i.e., desires), and because Tom has no desires (aside from keeping his wife Goldberry happy), the Ring simply couldn't reach Tom. He is entirely beyond its influence, and it is just another piece of jewelry to him.
Resumo:
The Ring inspires the person who bears it to become pathologically possessive of it, because it has a better chance of being found by its master if someone has it. But as soon as the Ring realizes that its current keeper is no longer useful to its goal of returning to Sauron, it abandons him and finds its way to a new keeper. The Ring is in control at all times, and its only ambition is to find its way back to Sauron's hand. Its power comes from its ability to appeal to the individual's personal weaknesses (i.e., desires).
The information above is taken from the stories themselves (aside from the quote from Foster's Complete Guide to Middle-earth). I just finished doing some searches on Tolkien Gateway and in Tolkien's letters, and found the following info:
Tolkien Gateway:
Part of the nature of the Ring was that it slowly but inevitably corrupted its wearer, regardless of any intentions to the contrary. Whether this was specifically designed into the Ring's magic or is simply an artifact of its evil origins is unknown. (Sauron might be expected to endow his One Ring with such a property, but he probably never intended anyone besides himself to wear it. It may be a side-effect of the portion of Sauron's will that lies within the Ring, influencing the wearer.) For this reason the Wise, including Gandalf, Elrond and Galadriel, refused to wield it in their own defence, but instead determined that it must be destroyed. It appears that Hobbits, being more pure of heart than Men, and far less powerful than Elves, were the ideal vessels to resist its seductive power; this explains why Frodo and Bilbo bore it for long periods of time with very little ill effect. Even Gollum had not turned into a Wraith after 500 years of bearing the Ring.
The enigmatic Tom Bombadil was unaffected by the Ring, or rather, the Ring had no effect on him. This may be explained in many ways. (See the article on Tom Bombadil, which includes some theories.)
Letter #109:
You can make the Ring into an allegory of our own time, if you like: an allegory of the inevitable fate that waits for all attempts to defeat evil power by power. But that is only because all power magical or mechanical does always so work. You cannot write a story about an apparently simple magic ring without that bursting in, if you really take the ring seriously, and make things happen that would happen, if such a thing existed.
Letter #131:
The Ring was unbreakable by any smithcraft less than his own. It was indissoluble in any fire, save the undying subterranean fire where it was made – and that was unapproachable, in Mordor. Also so great was the Ring's power of lust, that anyone who used it became mastered by it; it was beyond the strength of any will (even [Sauron's] own) to injure it, cast it away, or neglect it. So he thought. It was in any case on his finger.
A moral of the whole (after the primary symbolism of the Ring, as the will to mere power, seeking to make itself objective by physical force and mechanism, and so also inevitably by lies) is the obvious one that without the high and noble the simple and vulgar is utterly mean; and without the simple and ordinary the noble and heroic is meaningless.
But to [make the Ring, Sauron] had been obliged to let a great part of his own inherent power (a frequent and very significant motive in myth and fairy-story) pass into the One Ring. While he wore it, his power on earth was actually enhanced. But even if he did not wear it, that power existed and was in 'rapport' with himself: he was not 'diminished'. Unless some other seized it and became possessed of it. If that happened, the new possessor could (if sufficiently strong and heroic by nature) challenge Sauron, become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place. This was the essential weakness he had introduced into his situation in his effort (largely unsuccessful) to enslave the Elves, and in his desire to establish a control over the minds and wills of his servants.
With the aid of Sauron's lore [the Elven smiths] made Rings of Power ('power' is an ominous and sinister word in all these tales, except as applied to the gods).
Letter #153:
Also T[om] B[ombadil] exhibits another point in his attitude to the Ring, and its failure to affect him. You must concentrate on some pan, probably relatively small, of the World (Universe), whether to tell a tale, however long, or to learn anything however fundamental – and therefore much will from that 'point of view' be left out, distorted on the circumference, or seem a discordant oddity. The power of the Ring over all concerned, even the Wizards or Emissaries, is not a delusion – but it is not the whole picture, even of the then state and content of that pan of the Universe.
Letter #181:
Frodo was in such a position: an apparently complete trap: a person of greater native power could probably never have resisted the Ring's lure to power so long; a person of less power could not hope to resist it in the final decision. (Already Frodo had been unwilling to harm the Ring before he set out, and was incapable of surrendering it to Sam.)
Letter #191:
If you re-read all the passages dealing with Frodo and the Ring, I think you will see that not only was it quite impossible for him to surrender the Ring, in act or will, especially at its point of maximum power, but that this failure was adumbrated from far back. He was honoured because he had accepted the burden voluntarily, and had then done all that was within his utmost physical and mental strength to do. He (and the Cause) were saved – by Mercy : by the supreme value and efficacy of Pity and forgiveness of injury.
Letter #211:
You cannot press the One Ring too hard, for it is of course a mythical feature, even though the world of the tales is conceived in more or less historical terms. The Ring of Sauron is only one of the various mythical treatments of the placing of one's life, or power, in some external object, which is thus exposed to capture or destruction with disastrous results to oneself. If I were to 'philosophize' this myth, or at least the Ring of Sauron, I should say it was a mythical way of representing the truth that potency (or perhaps rather potentiality) if it is to be exercised, and produce results, has to be externalized and so as it were passes, to a greater or less degree, out of one's direct control. A man who wishes to exert 'power' must have subjects, who are not himself. But he then depends on them.
Letter #246:
[A reply to a reader's comments on Frodo's failure to surrender the Ring in the Cracks of Doom.]
Very few (indeed so far as letters go only you and one other) have observed or commented on Frodo's 'failure'. It is a very important point.
From the point of view of the storyteller the events on Mt Doom proceed simply from the logic of the tale up to that time. They were not deliberately worked up to nor foreseen until they occurred. But, for one thing, it became at last quite clear that Frodo after all that had happened would be incapable of voluntarily destroying the Ring. Reflecting on the solution after it was arrived at (as a mere event) I feel that it is central to the whole 'theory' of true nobility and heroism that is presented.
Frodo indeed 'failed' as a hero, as conceived by simple minds: he did not endure to the end; he gave in, ratted. I do not say 'simple minds' with contempt: they often see with clarity the simple truth and the absolute ideal to which effort must be directed, even if it is unattainable.
I do not think that Frodo's was a moral failure. At the last moment the pressure of the Ring would reach its maximum – impossible, I should have said, for any one to resist, certainly after long possession, months of increasing torment, and when starved and exhausted. Frodo had done what he could and spent himself completely (as an instrument of Providence) and had produced a situation in which the object of his quest could be achieved. His humility (with which he began) and his sufferings were justly rewarded by the highest honour; and his exercise of patience and mercy towards Gollum gained him Mercy: his failure was redressed.
When Sauron was aware of the seizure of the Ring [by Frodo inside Mount Doom] his one hope was in its power: that the claimant would be unable to relinquish it until Sauron had time to deal with him. Frodo too would then probably, if not attacked, have had to take the same way: cast himself with the Ring into the abyss. If not he would of course have completely failed.
[Asked if Frodo, after claiming the Ring as his own inside of the volcano, could have used it to fight off, or even command, the Nazgûl and use them against Sauron: Tolkien says the Nazgûl would have pretended to obey Frodo, and probably wouldn't have attacked him...]
Until Sauron himself came. In any case a confrontation of Frodo and Sauron would soon have taken place, if the Ring was intact. Its result was inevitable. Frodo would have been utterly overthrown: crushed to dust, or preserved in torment as a gibbering slave. Sauron would not have feared the Ring! It was his own and under his will. Even from afar he had an effect upon it, to make it work for its return to himself. In his actual presence none but very few of equal stature could have hoped to withhold it from him.
[Regarding how Galadriel was able to resist the lure of the Ring]
It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power. But this the Great had well considered and had rejected, as is seen in Elrond's words at the Council. Galadriel's rejection of the temptation was founded upon previous thought and resolve.
Gandalf's explanation of why Bilbo was more or less unharmed by his long tenure as the Ringbearer; Frodo has just made clear his disgust at Bilbo for taking pity on Gollum. Gandalf explains that this is why Bilbo wasn't destroyed by the Ring:
'"Pity? It was Pity that stayed [Bilbo's] hand. Pity, and Mercy: not to strike without need. And he has been well rewarded, Frodo. Be sure that he took so little hurt from the evil, and escaped in the end, because he began his ownership of the Ring so. With Pity."'
This obviously means that the intent of the bearer is crucial to his eventual fate after bearing the Ring. If you begin your time as Ringbearer with pity for unfortunate souls like Gollum, the Ring has less effect on you. This is very reminiscent of the Ring's tendency to amplify the bearer's personality - if you are already thirsty for power, the Ring will corrupt you almost immediately, as it did to Boromir, and as it did to Saruman despite the fact that he had never even seen it, or been anywhere near it at any time.