Why are trilogies so prevalent in Fantasy?

Here are three reasons:

1. Fantasy stories need to go into details that real-world-based fiction doesn't: cultures, politics, religions, biology, magic, science, technology, you name it. And part of the fun of it is exploring a completely fantastic setting where all the rules are different; when you take out that exploration, I think you'd get something much closer to magical realism.
2. As jwenting points out, epics go well in a trilogy format. It's a rare writer and story that can get away with more. And if an author can get people to buy into book two, why not write three?
3. Fantasy readers, I think, are much more likely to be reading for the fun of it than the general public, and are much more likely to be tolerant and accepting of a story that doesn't finish in one book. Meanwhile, if your main goal in reading a book is to pass five hours on an airplane, you aren't going to pick up a three-volume doorstopper.

Well firstly, most fantasy genres are single books, not trilogies or otherwise. That being said, assuming a book is popular enough to be made into a sequel, it's usually spanned into three books because most publishing companies will try to maximize profits in this way.

Consider also the rule of three. Three is typically considered a "well-rounded" number for what concerns stories because it represents a beginning, middle, and end.

Many epics take more space than a publisher is willing to publish in a single volume. As customers have gotten used to the trilogy format, that thus becomes a good target to aim for when writing something that won't fit in say 300-450 pages. Make it a 2 volume series, and people will wonder when part 3 will be published, Make it a 4 part series and you get complaints after part 3 that it's "unfinished".
Tolkien has nothing to do with that, trilogies have existed long before he wrote his masterpiece (which was originally released as a series of 7 books btw, not a trilogy, only later were those 7 volumes combined with appendices released as a 3 volume set).

Note: We had a very similar question on Writers.SE; I'm cross-posting my answer from there, adjusted to your specific question.

I think the reason for the popularity of the trilogy structure in the fantasy genre is simply that fantasy novels tend to be longo. This occurs for for many reasons, including:

• Fantasy novels typically require lots of world-building exposition, explaining the setting, the mechanics of magic, central factions in the world, etc. etc.
• Fantasy novels are often interested in exploração; showing off various fantastical elements (places, creatures, magic items...) is often a lot of the book's focus. So the narrative is designed with a lot of shifting from place to place, and introducing new elements very frequently.
• Fantasy novels often have epic plots, about the rise and fall of kingdoms and dragons and deities. Epic plots tend naturally to be of greater length, because this gives both time and wordcount to properly build up this epic scope. Readers will probably not care much whether the Empire of Lime can defeat the Bespectacled Dragon unless they've gotten a sense of all these elements as being rich, intriguing, and with real substance.

Since fantasy tends to expand into great length, multi-book structures are necessary. The moment that's a given, trilogies are a natural choice -

• it's a short, well-defined series;
• that's a length fantasy readers will be willing to risk dipping into;
• the three-book structure can, in many senses, duplicate the three-act structure;
• it's a short as you can get besides a duo (which - maybe this is just me - feels like an awkward length, which needs to work harder to justify the split into multiple books, and is harder to structure a single narrative around).

Em outras palavras, trilogies are popular because they're "short" (compared to longer sagas), não because they're long (compared to stand-alones). I think you'll find that stand-alones are actually easier sells, both to publishers and to readers - they'd much rather buy/read something complete, self-contained, and non-risky. It's simply that such books are less common, particularmente when a lot of genre fans are interested in fantasy specifically for the length-inducing elements I've mentioned (world-building, exploration, epic plots).

Most modern storytelling follow a Three act structure. Epics and series often have micro plots (plots that develop and resolve internal to the "episode"), and macro plots that span the entire story (also known as major and minor story arcs). As a story expands, the structure stays fairly constant, and can become a fractal of the three act design. So therefor, the entire story fits into three acts, or three books/movies/whatever, and each piece is itself a three act process.