BTW, they made a TV version of this a few years back. DO NOT watch it! It completely butchers the whole point of the story – the cold equations are a government lie to keep control of the pilots.
My favorite is Burning Chrome by William Gibson. Classic Cyberpunk, and I wish he had never moved on from Cyberpunk, or at least to what he is up to lately…
“Scanners Live in Vain” by Cordwainer Smith
(I’m only putting down one, because if I put down any more, I’ll be typing for a very long time.)
I haven’t seen a vote for “Far Centaurus” by A. E. van Vogt.
A space ship sets out for the nearest star system with the astronauts in hibernation, only to arrive at their destination to find that technology has passed them by, and the worlds there are already populated by…Earth people who discovered faster ways to travel, after they had left.
It illustrates a paradox, and I’m sure there is a name for it but I can’t put my finger on it right now, of why should we send ships on long voyages that will only become obsolete in the near future when better technology is discovered.
If you don’t send the slow ships now, the new technology might not be discovered, if you do send them they may be passed up and forgotten.
So do you go now, or do you wait?
Too late to edit. I just realized that this thread was started before I registered to post here.
It’s like this thread woke up and time had passed it by.
I see what you did there. 
But, if we can still play, I would like to nominate Common Time by James Blish and Day Million by Frederick Pohl.
My favorite, not mentioned, is Mother Hitton’s Littul Kittons, by Cordwainer Smith. Unfortunately I cannot seem to find it online.
Blood Music by Greg Bear. It’s both a short story and a novel. Both are wonderful.
I’d vote for so many of those already mentioned. But I’d like to add “Rogue Moon” by Algis Budrys . This was also in the Science Fiction Hall of Fame . It has an unforgettable ending.
“Placet Is A Crazy Place”
Just noticed this thread. Very hard to narrow down my many favorites, but with great self-restraint I’ll list, say, my top five:
“The Moon Moth” by Jack Vance - An Earth diplomat offends the local alien populace, all of whom wear masks and communicate by singing, while trying to catch a criminal.
“Sandkings” by George R.R. Martin - A bored, dissolute rich man acquires alien pets - a culture of tiny warriors who will teach him a deadly lesson.
“The Scythe” by Ray Bradbury - During the Depression, a down-and-out man and his family find a peculiar farm, and he soon realizes he has met a most unwelcome destiny.
“Little Lost Robot” by Isaac Asimov - Dr. Susan Calvin must find a particularly wily - and dangerous - robot which is purposefully hiding on a military asteroid base.
“Rescue Party” by Arthur C. Clarke - An alien starship comes to help the people of Earth just before the Sun goes supernova… and its crew gets a surprise that will reverberate for years to come.
I could think of another five - or twenty - without too much effort. But these are particularly good, and particularly close to my heart.
It’s been mentioned, but the SF short that’s considered a classic and has stood up best for me is PKD’s “Second Variety”. Given the Cold War setting it may not be as timeless as some others mentioned, but I don’t really feel that SF lends itself well to timelessness. Fantasy, which is not dependent on the current understanding of how the universe works, does timeless a lot better than SF.
“Second Variety” reflects its time in the classic SF way: 50s paranoia. However, rather than a conspiracy of communists hatching plots to overthrow Americans, a conspiracy of robots is plotting to overthrow both the commies and the yanks, throwing out the whole thing. Naturally, the protagonist can’t tell real from fake. The robots don’t just plot against the humans, either; there’s evidence that they’re gearing up to wage war on one another. It speaks to the human condition in a way that SF only can: humans can, through science, not only destroy themselves, but create the destroyers and provide them with tools.
I’ve read most of these and agree with your assessment. I also like Sturgeon’s “Baby is Three” and “And Now the News,” Tenn’s “Brooklyn Project” and Heinlein’s “The Roads Must Roll”.
I love that story! Hilarious. Funny sf at its best.
It draws the perfect distinction between aliens who know everything and have much to teach humanity, and aliens who… are just annoying know-it-alls.
Came here to post this.
I’ll throw “The End of the Whole Mess” by Stephen King into the mix.
Weird, it’s, like, the second link if you Google-search the name.
Thank you. I have this argument far too often.
In other news, I have on my shelf a collection entitled The Best Time Travel Stories of the 20th Century that includes neither “By His Bootstraps” NOR “All You Zombies”. What a joke! I mean, I understand that you can’t always buy the rights to the stories you want, but the collection is incomplete without one of those two stories.
There are several stories that were totally original when they were written but now suffer because the concepts have been copied so many times since by lesser writers.
I was lucky enough to read Heinlein’s Universe and Weinbaum’s A Martian Oddessy at a very young age before being exposed to any of the poor imitations that followed and consider those two stories to be the best short SF I’ve ever read. The Golden Age of Science Fiction is, indeed, the age of 10.
I’ll mention a few of my favorites that I don’t think anyone has mentioned yet;
The Jaunt, Stephen King
The Weapon Shop, A.E. van Vogt
Born of Man and Woman, Richard Matheson
Button, Button, Richard Matheson
It’s a Good Life, Jerome Bixby
SCP-093, various authors
well I’m not sure about the short story size requirement but The Light of Other Days is a story about how a single invention can unwind all cultures everywhere as we know it.