Oh, good one!
“Not Final” makes the same point as the so-called Clarkes Law – “Whenever an established and highly respected scientist says that something is impossible, he is almost certainly wrong” – in a very dramatic manner.
Lots of Heinlein.
Personal favorite And He Built a Crooked House
Once again its a link to the actual story
Another vote for “Nightfall”. A big factor is the natural suspense.
I’m glad Cordwainer Smith stories have been mentioned, but there are others I like better: “The Game of Rat and Dragon”, “Think Blue, Count Two”, and “A Planet Named Shayol”.
In the versions I’ve read, the last line is “A boy loves his dog.”
For the all-around best, I’d have to say Niven’s “The Inconstant Moon”. It’s a very good soft SF story, except that it just happens to be rigidly hard SF. Or, as others have said, the science doesn’t get in the way of the characters.
Another Niven which hasn’t been mentioned yet, but should be, is “The Hole Man”. I don’t think it’s his best (see above), but it’s very good, and well-grounded both in real people and real science (it’s now outdated, but in a way that Niven couldn’t possibly have forseen).
As a personal favorite, I’ll add to the votes for Heinlein’s “By His Own Bootstraps”. Speaking as someone obsessed with time travel, I can without hesitation say that it’s the best time travel story ever written, or ever likely to be written. “All You Zombies” is also very good, but it can’t possibly be the best, since in every way that it’s good, “Bootstraps” is better.
Finally, if you’re looking for good stories collected together, I’d recommend the anthology series of the Hugo winners. The Hugo is the most prestigious award in science fiction (except possibly for the Nebula, but I think that the Hugo choices are much better), and the early volumes were edited by Asimov.
Pah, amateurs, all of 'em.
They can’t hold a candle to Jim Theis’s THE EYE OF ARGON.
All hair Grignr!
Thirded.
Mrifk! I’d wondered if someone would bring that up. 
Okay, It’s been a very long time since I read the story. I may have confused the last line in the story with the last line from the movie (which I just saw a few months ago). Either way, it’s a great story, and it makes me giggle every time I read it.
Because I lack the motivation to do anything more constructive with my time, at 5PM US Pacific Standard Time tonight (1/28/05), I will tally all the votes and nominations from this thread and present a top ten list of which stories are the most popular.
Coo…
Put me down for 10,000 votes for The Eye of Argon.
Red emeralds. [Unintended] comedy gold.
squeeeeaks in I’m going to throw in three, all of which have already been mentioned:
Asimov’s The Last Question and Nightfall, and Bradbury’s All Summer In a Day.
Ok, here are the top ten stories:
There were some ties:
#1 (6 votes each)
*Nightfall *- Isaac Asimov
Inconstant Moon - Niven
#2 (5 votes each)
Flowers for Algernon - Daniel Keyes
The Cold Equations - Tom Godwin
The Last Question - Isaac Asimov
#3 (4 votes)
The Star - Arthur C. Clarke
#4 (3 votes each)
I Have No Mouth and I Must Scream - Ellison
By His Bootstraps - Heinlein
Faith of Our Fathers - Philip K. Dick
All Summer in a Day - Ray Bradbury
I believe you are referring to “Rescue Party,” Clarke’s first published story. Lots of people consider it his best - he wrote somewhere that this makes him kind of depressed, as if he never improved.
I’m not sure the tabulated votes are valid - I think lots of us were trying to come up with new nominations. Can I add a vote for “Flowers for Algernon?” “The Last Question” is a cute story, but more of a gimmick than a real story.
Hi. Space Western != Science Fiction. Ergo, bite me. 
It didn’t occur to me that some considered Flowers for Algernon as science fiction until it appeared in this thread. I’d have to re-read the short story (and probably read the novelization, too) before I chime in on whether I still don’t consider it SciFi. I merely said I liked it (relative to the other reading material available in the textbook, mind you), BTW, not that it was good.
I don’t think I’d classify it as speculative fiction. It’s primarily a character novel tracing a single man’s journey. Not about how technology will impact society or any of the other themes that earmark “real” science fiction or speculative fiction. I guess you might sneak it in by pointing out that pharmacological research is a science, but so is urology… (if anyone has an example of some SciFi where the science is urology, I’d love to hear it)
I will add yet another vote for “Flowers for Algernon” and would like to mention (for the first time in this thread, I believe) Robert Heinlein’s “Requiem” and Harry Bates’ “Farewell to the Master.”
Allamagoosa by Eric Frank Russell. He’s not a well-known writer, but it’s such an exceptional (and hilarious) short story that it’s the first one that came to mind, followed close behind by Clarke’s The Star and Asimov’s It’s Such A Beautiful Day.
I’m not entirely sure that it qualifies, but the first thing that came to mind when reading this comment is “The Generic Rejuvenation of Milo Ardry” by Elizabeth Moon.
It is a short story focused on a rich man who develops a desire for frequent rejuvenation based on his desire to urinate like a young man. (or something like that. It is difficult to write in a manner which I am willing to have my name associated with.)
For the record, while I remember it as an enjoyable story, I’m not sure I’d list it as a best science fiction short story, even ignoring the minor detail that I’ve never read most of those nominated by others.
As a young man, Daniel Keyes became associate editor of Marvel Science Fiction magazine in 1951. He published several of his own early works in that magazine, a not-unusual practice of the day.
Later, in the late 1950s and early 1960s, he published several more stories in Galaxy Science Fiction, If, The Magazine of Fantasy and Science Fiction, and Worlds of Tomorrow.
In that span, he also published, in the April 1959 of The Magazine of Fantasy and Science Fiction, a novelet titled “Flowers for Algernon.” That was a pretty good issue, BTW. It featured Poul Anderson’s classic Sherlock Holmes pastiche “The Martian Crown Jewels,” as well as stories by Isaac Asimov, Gordon R. Dickson, Frederik Pohl, Anne McCaffrey, and some guy named Anton Chekhov doing a parody of Jules Verne.
Still, out of all those names, it was Daniel Keyes who won the Hugo Award for Best Short Fiction the next year, over the likes of Philip José Farmer, Theodore Sturgeon, and Alfred Bester.
Later, when Keyes expanded the story into a novel in 1966, he picked up a nomination for Best Novel in the Hugos. He did slightly better in the newfangled Nebula Awards, presented in 1966 for only the second time by the Science Fiction Writers of America. Flower for Algernon tied for Best Novel with Samuel R. Delany’s Babel-17. The novel that came in third place that year was Robert A. Heinlein’s The Moon Is a Harsh Mistress.
Let’s recap. A career science fiction writer published in a science fiction magazine a story about an impossible medical procedure which involved technology still not available to us 46 years later.
But it’s not science fiction because it’s about character?
I’ve been fighting this fight for 30 years now, and I’m tired, and disgusted that it still has to be fought. But I’m willing to give it one more try.
Good science fiction is good fiction. Good science fiction, like any good fiction, is first and foremost about character. Not about ideas. Not about inventions. Not about spaceships. Not about “how technology will impact society.” About character. The absolute best science fiction takes fully-wrought characters and places them in a world that is not ours, but is an extension, or an alternative, or a warning to our world, and shows how we, as fragile and amazing human beings, would be affected by that world. And if the fiction is very, very good, that world will affect us as readers as well.
That’s science fiction. That’s why “Flowers for Algernon” is a classic. That’s why it was made into a TV drama and a movie and even a musical (Michael Crawford played Charly in the original London production). That’s why the book is still in print - in hardback - and why there are student versions and teacher study guides and a whole academic apparatus - even a CliffNotes version - wrapped around it.
“Flowers for Algernon” is speculative fiction, although in the sense that Heinlein coined the phrase for, not the sense that I’ve been using it in. “Flowers for Algernon” is science fiction. The story could not happen without the science; the science is integral to the story. Neither belong to our world, but they’ve close, so very close, that we think, we hope, that we can reach out and touch Charlie Gordon, and feel for Charlie Gordon, and for ourselves.
That’s good fiction. That’s good science fiction.
And always will be.
Quarantine by Arthur C. Clarke has a very high ratio of “goodness”/word, because it is only 180 words!
For Flowers for Algernon? Or against the space western conception of science fiction? Or for the idea that good realistic fiction, which generally is difficult to classify, can still be pigeonholed into neat categories if we try hard enough?
Like I said, I’d have to re-read the short story. I didn’t recognize it as science fiction at the time. That fact that he wrote science fiction, published this story in the science fiction magazines he managed, and won a SciFi award for it (which may stem from the fact that it was a short story published in a SciFi magazine, not because it was a SciFi short story published in a magazine). I have not read the novel, seen the movie, etc. etc. those may indeed be recognizable SciFi… subsequent SciFi adaptations of the short story would not make the short story into SciFi if it is not. But like I said, I’d have to re-read it… on first exposure though, it never occurred to me that it was science fiction.