Oh I do love book threads ...
My favorite fantasy authors are (JKR excluded) Tolkien, Pratchett, Pullman and Eddings. I still haven't managed to read anything by Douglas Adams but it's on my list (which gecko will tell you is quite never-ending, thoguh

). Pratchett's Discworld series just crack me up on end, they're great if you want just something light to take your mind off of things and have a good laugh. Plus there are so many of them you are very unlikely to run out of reading!
Philip Pullman's His Dark Materials trilogy is possibly the very best fantasy I've ever read. Possibly. It's complex enough to hold one's imagination and the imagination of the guy is amazing! And the endling ... *sigh* I won't say anything in case you want to read hte books yourself but it's very touching, I almost cried.
David (and Leigh) Eddings write very good basic fantasy with lovable characters and a great sense of humor. Upto a certain point. I've read all of their published fantasy books (many several times) and it does tend to get slightly repetetive. For example the Redemption of Althalus I forced myself to finish, but it didn't offer anything new ot me. All the jokes, the events and almost the characters were just recycled material from their previous books. But anyway, my favorites are the Belgariad and everything related (i.e. The Mallorean, Belgarath, Polgara, the Rivan Codex). The Tamuli and the Elenium I never really liked and Althalus, like I said, was nothing new. If you're only starting to read Eddings I'm sure it's a good book, but for someone who's been reading him for almost ten years it's just boring.
Other authors and books I really are Austen, the Brontës, Burnett, Montgomery, Alcott and the sort; Dances with Wolves by Blake, Wilde, C. S. Lewis, Lewis Carrol, Seven Years in Tibet by Harrer, Woolf, Hawking, and others.