High Fantasy - def. Generally inspired by Lord of the Rings, this category is the largest and tends towards the epic, multi-book series.
1. The Belgariad, by David Eddings:
Book names: The Pawn of Prophecy, Queen of Sorcery, Magician's Gambit, Castle of Wizardry, Enchanter's End Game
Why I like them: This series is my go-to comfort series - again, I first read them when I was young. The premise is fairly standard for fantasy - boy, prophecy, quest, etc. - but Eddings infuses it all with very vivid characters and a good sense of humor. The world-building is meticulous and the plot is fun. If you read other series by him, I do have to admit that Eddings recycles both characters and plot, but I love them enough that I don't care for the most part.
2. The Riftwar Saga, by Raymond Feist:
Book names: Magician: Apprentice, Magician: Master, Silverthorn, A Darkness at Sethanon
Why I like them: These books are big, really big, in the epic sense. Feist builds two complete worlds - Midkemia, which is a familiar Middle Earth-type, and Kelewan, which is more alien and has Asian-style influences. His characters follow a more unique set of arcs than is typical for high fantasy and yet retain their core likability. There's more darkness and danger in this series than my other recs, but it's all very engrossing and I highly recommend it. There are several more series that Feist set in this world - personally, I like the Empire books (written with Janny Wurts) and Princes of Krondor, but the others I could take or leave.
Heroic Fantasy - def. Story centers around a hero and a quest generally. This genre has significant overlap with High Fantasy.
1. The Prydain Chronicles, by Lloyd Alexander:
Book names: The Book of Three, The Black Cauldron, The Castle of Llyr, Taran Wanderer, The High King
Why I like them: I first read this series when I was 8 or 9. It's geared towards a younger audience, but still holds up twenty years later. It uses elements from Welsh myths and legends, which gives it an aura of authenticity and a sense of a larger world. The characters noticeably develop from the first book to the fifth and they're all very vivid. Taran, the protagonist, and Eilonwy, the princess, are appealing and probably the first 'ship I ever fell for.
2. Sabriel, Lirael, and Abhorsen, by Garth Nix:
Why I like them: This is series is one of the more unique set of books that I've ever read. Nix came up with an extraordinarily interesting idea for magic - it's all linked to Death and controlled by ringing bells - and ran with it. The protagonists are female, which is a nice change of pace from most fantasy, and there's none of the annoying gender battle crap which tends to mar other fantasy - they're just female with their own special powers. Really, I cannot recommend these books highly enough.
Comic Fantasy - def. Fantasy that's funny. It's kind of self-evident.
1. MYTH Adventures, by Robert Asprin:
Book names: Several, but here are the first few: Another Fine Myth, Myth Conceptions, Myth Directions, etc.
Why I like them: Well, like any good comic fantasy, they're FUNNY. Asprin sprinkles the books with puns, situational comedy, and even has time for some character development and real plot. Skeeve is the sweet, slightly dim, apprentice wizard and Aahz (no relation) is his gruff, scaly, inadvertent mentor who's lost all his powers. The books take you through several adventures, several dimension, and generally just entertain.
2. Good Omens, by Neil Gaiman and Terry Pratchett:
Why I like it: Gaiman and Pratchett are both incredibly entertaining writers, so putting them together was bound to produce something good. They're also both very British, so the comedic style is a little different than what most of us Americans are used to. This book is all about the Anti-Christ and the coming Apocalypse and all the things that go terribly wrong along the way. There are mix-ups, and mistakes, and misunderstandings, and coincidences, and it's all very, very funny.
Contemporary Fantasy - def. Fantasy set in the modern day and age.
1. The Dark is Rising, by Susan Cooper
Book names: Over Sea, Under Stone, The Dark is Rising, Greenwitch, The Grey King, Silver on the Tree
Why I like them: These are some of the best young adult fantasy books ever written and they're still entertaining for adults. If not for the contemporary setting, this series also fits into the High Fantasy genre as they're structured around an epic, on-going battle between the Light and the Dark. What I love is how Cooper incorporates elements from Arthurian myths, as well as Celtic and Welsh ones. The first book is probably the weakest of the lot, but the second can be read as a stand-alone if you wish to skip ahead.
2. War For the Oaks, by Emma Bull
Why I like it: While the premise of the book is built around a war among Faerie, at it's heart, this book is a personal one. It's a bit about a band and the lead Eddie (female) and a bit about a love story. The cross-over between the magical world and our own is handled gracefully. Over all, an engaging read.
Historical Fantasy - def. Fantasy centered around a particular historical time period not our own.
1. Sorcery & Cecilia or The Enchanted Chocolate Pot, The Grand Tour, and The Mislaid Magician, by Patricia Wrede and Caroline Stevermer
Why I like them: Take Jane Austen, add magic, and you pretty much have these books. The first book started out as a letter game between the authors - they wrote letters to each other in character without discussing the plot beforehand. The plot grew quite organically and they ended up with a unique and entertaining book. Of the two sequels, the third is better than the second, but I love all three.
2. Temeraire, by Naomi Novik
Book names: His Majesty's Dragon, Throne of Jade, Black Powder War, Empire of Ivory
Why I like them: If you ever thought that what the Napoleonic Wars were missing were dragons, then these are the books for you. Dragons are pretty much war beasts for the English and the French, but they're also intelligent in their own rights. I'm normally not a fan of dragon-centered books, but Novik does a wonderful job here in building a reasonable set of advantages and limitations to having dragons around. At its core, I suppose, these books are really all about a man and his dragon.
This is not even close to an exhaustive list of stuff to read, but hopefully you found something new. Do me a favor - if you're ever in Berkeley, stop by The Other Change of Hobbit on Shattuck Ave. It's a small independent fantasy book store with a very helpful staff who recommended several of these books to me originally.