I am, of course, a huge fan of Jack Vance, so a large part of his output would make the list. However if I had to narrow it down, the Dying Earth series and four of his novellas: "The Dragon Masters," "The Last Castle," "The Miracle Workers," and "The Moon Moth" would all make the list. "The Moon Moth" is the only one of those that doesn't take place in a far-future, technologically regressed society, and if I had to pick just once Vance story that would be it.
Aside from Vance, Ursula LeGuin's The Dispossessed and The Left Hand of Darkness absolutely have to make the list, as does "Flowers for Algernon" (note that I only read the novella). I'd really consider everything in the Science Fiction Hall of Fame essential reading. It was picked by the same people who pick the Nebulas, but selection was much more competitive and it was further winnowed by Robert Silverberg. Though some of the best pre-1965 SF was left out, everything in it is absolute gold. I know of no other anthology which I'd argue meets that standard, so I won't suggest any others (besides, we have a thread for anthologies).
After that, I'd like to nominate three really unusual novels: Rendezvous with Rama by Arthur C. Clarke, Evolution by Steve Baxter, and The Crucible of Time by John Brunner. The first one shouldn't be controversial because it's a classic which makes a lot of best-of lists, yet it has no plot and is simply an in-depth exploration of a bizarre alien spaceship. And yet it works somehow, and works really well. I didn't really like Evolution when I first read it, since it's really a collection of linked stories with again, little plot. But it's grown on me considerably since my first reading and I'd now consider it among my favorite books. The Crucible of Time describes the lifespan of an alien species, in its own terms, without the species ever encountering humanity. It's a bold thing to do, and I felt the book had a dreamlike feel to it. I consider it far superior to his best-known and most-liked book, which frankly feels rather dated.
I'd also like to bring up three novellas: "The Black Destroyer" by A. E. Van Vogt, "Exploration Party," by Murray Leinster, and "Turquoise Days" by Alastair Reynolds. All of these deal with alien-human interactions in interesting ways. I'll also mention L. Sprague DeCamp's "The Wheels Of If" which remains, to my mind, the greatest alternate history story ever written. Finally, I'd like to mention a few really powerful short stories which didn't make the SF Hall of Fame but I think are absolutely worth reading: "Goblin Night" by James Schmitz, William Tenn's "On Venus Have We Got a Rabbi" "Spacetime for Springers" by Fritz Leiber, "Your Haploid Heart" by James Tiptree Jr., "A Man of the Renaissance" by Wyman Guin, "The Ambassadors" by Anthony Boucher, and "The New One" by Fredric Brown. Each of these I found really striking in its own way, but since some of them have twist endings I won't reveal anything more about them.