First, some comments on books already mentioned:
Second on Dan Simmons' Hyperion and Fall of Hyperion. However, there's two more after that, isn't there? Endymion and...whatever. I hated those two. The first two are definitely worth reading. Consider stopping there.
Second on Jonathan Strange and Mr. Norrell. I recently reread it (and it's a huge tome) and it was wonderful. Fans of Neil Gaiman's work (such as the aforementioned American Gods and Good Omens) ought to check it out.
I recently reread the Foundation series and it's still a good read. It's really dated, though, in a lot of ways.
Now, some suggestions I haven't seen:
Octavia Butler's Parable of the Sower/Parable of the Talents. I love Octavia Butler's work, and this is a rare achievement. Parable of the Sower was already a great book and didn't need a sequel, but years later Butler went and wrote one and it's worthwhile. Depressing and optimistic at the same time.
Kim Stanley Robinson's Mars series (Red Mars, Green Mars, Blue Mars). Captivating reality-based science fiction about terraforming Mars. I wouldn't read them one right after another, as I got a little tired by the time Blue Mars is over. But they're great reads, and more than a little scary.
Mike Resnick's collected Kirinyaga stories, and the Oracle/Santiago/Soothsayer series. Kirinyaga is sci-fi fable-like stories, and all the stories are collected in one book and make a great story arc. Oracle is a terrific book, a little bit in the vein of Foundation but with a twist on that idea.
Ursula LeGuin's Earthsea series. Liked the TV version? Read the real thing, which is 1000x better. Read The Left Hand of Darkness and The Lathe of Heaven while you're at it.
Tad Williams' Otherworld series. Definitely the most detailed virtual reality saga. It's really overlong, though, and could be edited judiciously -- definitely another one to not read one after the other. But I'm glad I read them.
Alfred Bester's The Demolished Man and The Stars My Destination. Dedicated Babylon 5 weenie that I am, I picked up all the (real-life) Bester books when they were reprinted several years ago. They have nothing to do with B5, but they are astonishingly good science fiction.
Melissa Scott's Dreamships and Dreaming Metal. For most of her books, Melissa Scott creates a mix of intriguing (and typically clashing) social structures and technology, and then goes and creates a totally different world in her next book. Dreamships and Dreaming Metal are an exception, being sort-of sequels with mostly the same characters. These books are about AI. Burning Bright, another good one of hers, is (in a way) about online gaming.
Finally, the most astonishing book I've read lately is Susan R. Matthews' "An Exchange of Hostages". It's an examination of torture (but not torture-porn) in a sci-fi setting, and it's totally unsettling and yet totally captivating.