I'm a huge reader, particularly in fantasy and science fiction. Here are a few of my favourites: (some already mentioned are favourites of mine as well but I'll stick with those nobody has listed to avoid repetition)
FANTASY:
-"The Chronicles of Thomas Covenant" by Stephen Donaldson. Guy ends up teleported from the real world into a fantasy world and people think he is the reincarnation of their greatest hero. Incredibly well-written, though I will warn that the language is a bit difficult; you'll need to buy a dictionary when you get these. I wouldn't let younger children read these, though, as there are a few adult ideas; one of the major plot points is the rape of one character by the hero. 6 books from the late 70s/early 80s, and he's started another set of 4 books in the last couple years, but I haven't read the new ones yet.
-"The Wheel of Time" by Robert Jordan (being finished by Brandon Sanderson) Can't believe nobody said this yet. Absolutely epic fantasy series; literally hundreds of characters to keep track of; great fun! Sadly, RJ died a few years ago before completing the series, but his wife picked Brandon Sanderson to complete the last few books, and he's done a great job, not only with the writing itself, but even in managing to keep things in Jordan's style.
-"The Sword of Truth" by Terry Goodkind. Another one I can't believe nobody has mentioned. Another epic fantasy series, though with nowhere near as many characters as Jordan's novels, but no less good for that. I thought he'd finished the series, but apparently he's going to do at least one more novel in the near future.
-"The Shannara Series" by Terry Brooks. Does nobody in this thread read fantasy? :p I'm listing all of the greats here. (apparently the secret to success in fantasy writing is to be named Terry; Terry Goodkind, Terry Brooks, and Terry Pratchett have all made huge names for themselves in fantasy) Excellent series of novels and the ones that I blame for my epic fantasy addiction that began about age 12 when a friend recommended them to me.
-"Conan the Barbarian" by Robert E. Howard. (apparently Robert is also another good fantasy author name!) REH died at an early age (30s from suicide) but he still managed to write an awful lot of stuff, and other authors have written books in the Conan universe, such as L. Sprague de Camp. These are considered 'low fantasy' in that there isn't a lot of magic or wizards or that sort of thing; it's mostly Conan going around kicking ass and screwing women :p
-H.P. Lovecraft. Another author who died young (40s from some illness if I recall), he never wrote any novels, focusing exclusively on short stories, but damn can he write short story horror fantasy. He was called "the greatest horror writer of all time" by Stephen King. STEPHEN KING. Now THAT'S endorsement.
SCIENCE FICTION:
-"John Carter of Mars" by Edgar Rice Burroughs. More famous for creating Tarzan (which I haven't yet read) ERB also wrote these fun novels. They are a little bit silly and formulaic, being the literary equivalent of an action movie, but I liked them nonetheless.
-"Neuromancer" by William Gibson. This guy literally invented cyberpunk with this novel. Take the bleakness of Orwell's '1984' and imagine he'd lived to see the internet, and that's about the mood you get here.
"Otherworld" by Tad Williams. This is like "The Matrix" on steroids. A series of 4 books set roughly 100 years in the future, where the main plot is centered around a secret virtual reality construct. Williams also wrote some fantasy, notably "Memory, Sorrow, and Thorn", and is also worth reading, but "Otherworld" is much better, so I'm putting Williams in sci-fi.
"Eon", "Eternity", and, to a lesser degree "Legacy" by Greg Bear. Hard scifi at its finest. Not much in the way of aliens here, but quality scifi nonetheless. It's got everything; time travel, immortality, The Matrix-like computers, and everything else you'd want in science fiction. It's got a few aliens, too, but they are not the focus of the novels.
GENERAL FICTION:
"Atlas Shrugged" and "The Fountainhead" by Ayn Rand. These are rather philosophical works, but I thought they were masterfully written, and still relevant today; Atlas Shrugged's economic situation is almost as screwed up as our modern situation.
"Brave New World" by Aldous Huxley. This book is very often compared to "1984", so I'm surprised that was mentioned here and this one wasn't. If you liked 1984, you'll like this. Little known trivia: Huxley died the same day as JFK, but the assassination coverage overwhelmed news of his death.
Many of the other books in this thread I also recommend, but I won't do more than list them. Frank Herbert's "Dune", Raymond E. Feist's "Riftwar", Lord of the Rings by JRR Tolkien, Harry Potter by JK Rowling, Dragonlance (by various authors), Ringworld by Larry Niven, 1984 by George Orwell, Battlefield Earth by L Ron Hubbard, Ender's Game by Orson Scott Card (and basically anything else he's done) are all excellent choices in my opinion.