Seconded.
Damon Knight’s “To Serve Man” was great for the twist ending, but seems less so now that the whole world knows the punchline.
Aside from the Asimov shorts already mentioned, I’d have to add “The Dead Past.” It is great because it examines the full ramifications of a science-fiction gadget, and actually has believable characters with complex motivations (sometimes hard to find in Asimov, though by no means as rare as some say).
Several of Asimov’s robot stories could be included, though I’m not sure which I’d pick as the greatest. Probably the original, “Robbie.,” though most would find one they liked better somewhere in “The Complete Robot.”
Roger Zelazny - “For a breath I tarry”
“Dandelion Wine” By Ray Bradbury
The short story “Total Recall” was based on. “We Sell Memories Wholsale(?)” By Phillip K. Dick Also one of the funniest.
“We Can Remember It For You Wholesale” 
I’m a sucker for O. Henry type stories, including “To Serve Man.” I thought Fred Saberhagen’s early Berserker anthrologies were masterpieces of the art, although arguably not great science fiction. One of my favorite endings is contained in his “The Peacemaker” (if I remember correctly).
I’m sure somebody will come up with one after I post this, but I can’t think of a single great short piece of sf that benefitted by being expanded into a novel. Well, benefitted the reader. It surely benefitted the writer’s bank account.
There have been some works that turned into good novels because the author left the original piece as is, and just added new material to the end, but good short stories must be, almost by definition, complete of themselves with each word necessary and no others needed. It’s too bad the dynamics of the market won’t allow for that to be the end-all.
His anthologies weren’t bad either. :smack:
For these criteria, I think that Theodore Sturgeon fits the bill. Almost anything from his middle period on. (Check out the complete collection of his short stories, in progress, through North Atlantic Books.)
“Baby is Three” was the short story that spawned More Than Human.
It was said of Sturgeon that all of his stories were of love. It is hard to find one of his stories that does not contain at least a wisp of optimism or hope.
Contrast him with his friend, Harlan Ellison (well, Ellison called him a friend, but somehow I think that Sturgeon would have befriended even a rabid dog, so that is no great tribute). I know that Ellison is a force to be reckoned with, in print, TV, films and his own mind, and many of his stories have fascinated me, but I can only take so much before I choke on the bile.
No flame intended. There was a time when I read almost all of his work, but it means less to me as I grow older (criterion 1 above).
best to all,
plynck
“The Screwfly Solution” by Raccoona Sheldon.
The link is to the entire text.
“Shell Game,” “Foster, You’re Dead,” and “The Exit Door Leads In” by Philip K. Dick
“The Machine Stops” by E.M. Forster (I liked this one so much that I named my Livejournal after it)
“Tomorrow and Tomorrow and Tomorrow” and “The Euphio Question” by Kurt Vonnegut
“The Girl Who Loved Animals” by Bruce McAllister
“Tomorrow’s Child” by Ray Bradbury
“Shattered Like a Glass Goblin” and “The Human Operators” by Harlan Ellison (the second one listed A.E. Van Vogt as a co-writer)
I like what a lot of other people have listed, but didn’t want to relist anything. Also, thanks to whoever posted a link to “The Final Question” because I read that story years ago and loved it and forgot about it until now. I really should read more Asimov.
“Light of Other Days” by Bob Shaw
Delany’s “Time Considered as a Helix…” has also long been a favorite of mine.
2001 was expanded from a short by Clarke called “The Sentinel”. It also contained a bit of two other stories…
I don’t know if they were expansions of the short stories as much as novels that were inspired by short stories, but two of Philip K. Dick’s best novels, Do Androids Dream of Electric Sheep? and The Three Stigmata of Palmer Eldritch were based on short stories (respectively, “The Little Black Box” and “The Days of Perky Pat”).
Toss-up between Asimov’s Nightfall and The Dead Past.
Allow me a related question about tracking these stories down and enjoying them. How can a non sci-fi buff like me to read as many of these suggested stories as possible, while paying for the smallest number of different books, compilations, anthologies and so on?
With the exception of Asimov’s ‘The Last Question’, absolutely all the other stories mentioned thus far are new to me, and I’d like to sample them. I trust the Dopers’ judgement!
“Spook” by Bruce Sterling, from the Collection Crystal Express.
“It confirmed what I only suspected, being human just isn’t Fun enough”
Plus, everything from Sterling’s Shaper/Mechanist universe. *Schizmatrix Plus * is pound for pound the best Sci fi value I’ve ever personally purchased.
For those who don’t know, both Racoona Sheldon and James P. Tiptree Jr. were pseudonyms of Alice Sheldon.
I’d say that none of the three works named by BrotherCadfael or continuity eror are true expansions in the way that Flowers for Algernon or Behold the Man were.
Single authors have collections; multiple authors are combined into anthologies.
There are many thick anthologies of classic sf stories, really too many to name. However, a few suggestions.
David G. Hartwell has steadily put out huge books of major stories. Some of these include The Ascent of Wonder, The Evolution of Hard SF, The Hard SF Renaissance, Visions of Wonder : The Science Fiction Research Association Reading Anthology, and The Science Fiction Century. The last named is a standard work of the field.
If you have to limit yourself, though, it has to be The Science Fiction Hall of Fame, Volume I: The Greatest Science Fiction Stories of All Time, Chosen by the Members of the Science Fiction Writers of America, by Robert Silverberg and The Science Fiction Hall of Fame, Volume Two A : The Greatest Science Fiction Novellas of All Time Chosen by the Members of The Science Fiction Writers of America, by Ben Bova, undoubtedly the books with the most classics in the fewest pages. There are also a volume 2B, edited by Bova, and a volume 3, edited by Arthur C. Clarke and George Proctor, that are not in print, but should easily be available used.
I wouldn’t call 2001 an expansion, since there were totally different characters, the artifact is in a different place, and the Sentinel ends before the flight to the moon begins. I’d call an expansion a novel that ends where the story ends. Another example would be Silverberg’s Nightfall - definitely not a counter-example to Exano’s conjecture. A Canticle for Leibowitz worked as a novel, I thought, but it was the original story with other, later, stories added.
Damn, this thread makes me worry about my memory. Not just because I misremembered the title and author of my #1 pick (which is embarrassing,) but also because of the dozens of other first rate stories mentioned here that didn’t spring to mind. Time Considered as a Helix of Semi-precious Stones? Classic.
Another Le Guin: The Author of The Acacia Seeds, and Other Extracts from the Journal of the Association of Therolinguistics.
Up With The Queen!