Dragonlance. Start with Dragons of Autumn Twilight, then onto Winter Night then Spring Dawning. The next are the Time of the Twins, Test of the Twins then War of the Twins. After that comes Second Generation and then Dragons of Summer Flame. Then you have the War of Souls Series, which I can never keep those three straight, and the latest one by Margaret Weis is Amber and Ashes.
Horror? I know not. Good Dark Fantasy is always Anne Rice, she does a nice one. If you're good with vampyrs, go with Larry Niven and Ringworld, I heard that's a nice series.
Another fantasy is Piers Anthony and his Xanth novels. Don't bother which one, just read any. I suggest Golem in the Gears or Geis of the Gargoyle. His Incarnations of Immortality series is pretty good if you like a bit of mythology thrown into the mix. The first book of that is On a Pale Horse.
Tolkien is long and boring. Read the Tales of Tom Bombadil if you want to go with Tolkien. Other than that, not good.
Good fantasy worlds to get into: Krynn (Dragonlance books), Faerun (the dark elf series, and I believe the games of Baldur's Gate take place upon the Sword Coast of Faerun).
If you like satire, go with Anthony.
The Wheel of Time series is pretty good I've heard, by Robert Jordan. Lots of description, though; little action.
None of us can ever be free while others are still in chains. -Leslie Feinberg