Roger Zelazny. The entire humongous Amber series if you can, Lord of Light if you don't want to deal with a 10-book series. A Night in the Lonesome October as a very close second. (dammit, where is my copy of that???)

A random sampling of older stuff that comes to mind (well-known or not):

Tanith Lee, The Silver Metal Lover; CJ Cherryh's The Faded Sun trilogy or The Pride of Chanur and its sequels; Andre Norton's The Stars Are Ours and Star Born, or Sargasso of Space and Plague Ship (a fair amount of Norton is available free on Project Gutenberg); Heinlein is probably mandatory, perhaps Have Space Suit, Will Travel or Red Planet (the juveniles age better, I think); Leigh Brackett's Eric John Stark novels, The Ginger Star and its sequels (classic sf/fantasy space opera); Arthur C. Clarke's Childhood's End; LeGuin's Left Hand of Darkness; any Harlan Ellison collection from before 1985 or so; McCaffrey's Dragonflight; Asimov's Foundation trilogy (pretty much mandatory, I think).

I would also recommend Clifford Simak, who doesn't get much attention nowadays; H. Beam Piper; James H. Schmidt; Kate Wilhelm; C. L. Moore...

Hmm, brain needs more caffeine.

Thomas Covenant? That's ... different.

Short stories

• Asimov: “The Ugly Little Boy,” the robot stories collected in I Robot
• Bradbury: "A Sound of Thunder," "All Summer in a Day," "The Foghorn,"´(Hell, I might as well say, "All Bradbury short stories."
• Henry Bates, "Farewell to the Master"
• Jerome Bixby, "It's a Good Life"
• James Blish, "Surface Tension"
• Avram Davidson, "Or All the Seas with Oysters"
• Harlan Ellison, "Repent, Harlequin!" Said the Ticktockman," "I Have No Mouth, and I Must Scream," "The Beast that Shouted Love at the Heart of the World"
• Tom Godwin, "The Cold Equations"
• Cyril M. Kornbluth, "The Marching Morons"
• Ursula K LeGuin, "The Ones Who Walk Away from Omelas"
• C. L. Moore, "Vintage Season"
• Clifford Simak, the stories that make up City, some of which seem increasingly prescient
• James Tiptree, "The Women Men Don’t See"

(My brain had a formatting malfunction.)

Tiptree! Yes! And Bradbury! Sheesh. And Joanna Russ, if you feel like having your brain fucked with.

Definitely Tiptree! There was a really good collection of her short stories published about 20 years ago that I really liked. I can't remember the name of the story, but my favorite one was about the space freighter female worker who mutineed, killed the entire (male) crew, and then took the ship to a planet where the being with whom she had been subconsciously connected with all of her life lived. She couldn't live in the planet's atmosphere, so they just gazed at each other through the ship windows until she finally decided to venture out so they could touch briefly until she finally died from exposure.

Oh, "Vintage Season"! Yes!

And I don't know whether Shirley Jackson fits into fantasy, but she's definitely worth reading.

Some novels, as I think of them:

• Asimov, Foundation trilogy
• Arthur C. Clark, Childhood's End
• James Blish, A Case of Conscience, the Cities in Flight books
• Gordon Dickson, Soldier, Ask Not and maybe a few more Dorsai books
• Joe Haldeman, The Forever War
• Heinlein before he lost his marbles, including the juveniles (but not Podkayne of Mars), Starship Troopers, The Moon Is a Harsh Mistress, The Puppet Masters and Glory Road
• Vonda N. McIntyre, Dreamsnake
• Clifford Simak, City, Waystation, Time and Again, All Flesh is Grass, Why Call Them Back from Heaven?
• Fritz Leiber, Ill Met in Lankhmar
• LeGuin, The Left Hand of Darkness, The Lathe of Heaven

Does anybody really like reading Asimov? I think he's an incredibly shitty writer. His characterizations are weak. I know he's in the canon, but I would never recommend him.

Some of the robot short stories and that's it.

The short story is far and away Asimov's best form, but the Foundation trilogy was so influential (including inspiring Paul Krugman to be an economist) that it's de rigueur for an overview of the genre.

In regard to "The Cold Equations" - several years ago someone wrote a short story with the genders reversed (woman pilot, young boy) and solved the damn thing.