The first is far better than the second, but both are worth reading (and it’s Mote, BTW).
Thirded (fourthed?) as to Martin’s A Song of Ice and Fire series. Huge, gripping, sexy, violent, delightfully and eternally unpredictable.
Also check out Martin’s SF novel Tuf Voyaging (actually a collection of interrelated short stories). It’s a funny, bitingly satirical look at absolute power, ecology, war and overpopulation.
Another vote, too, for Ken Grimwood’s Replay, which I recently read for the first time after hearing it praised on NPR. A middle-aged guy dies of a heart attack in 1988 and finds himself back in college in 1963, able to live his life over again, but knowing what comes next… or does he? Fascinating and fun.
Dune by Frank Herbert, the first book in the ever-lengthening series, is great. All the rest suck, IMHO.
You’ve just gotta read J.R.R. Tolkien’s heroic fantasies The Hobbit and The Lord of the Rings, no question. Deservedly classics: incredibly rich, lyrical, fun, thrilling, bittersweet but uplifting books.
Asimov’s Foundation Trilogy, although somewhat dated now, is a big, fascinating series about the fall and rise of galactic empires.
Peter F. Hamilton’s Night’s Dawn Trilogy is also very big and ambitious (about a galactic empire dealing with… well, let’s just say a crisis), and stumbles badly at the end, but until you get there it’s good fun.
For Heinlein, you can’t go wrong with Starship Troopers, Time for the Stars, Have Spacesuit Will Travel, and The Moon Is A Harsh Mistress.