Great Short Science Fiction

Apropos of nothing other than listing them for the dusty annals of posterity, here's a list of the best science fiction short stories and novellas of all time I've ever read. It's the list I'd recommend to someone if they were seriously interested in the genre. I'm told making such lists is what blogs are for. Anyway ... as is obvious I've linked to text or pdf versions where I could find them, and annoyingly called them all "classics," listing them in no certain order:

• The Time Machine, H.G. Wells [link] [back-up link]
  The classic story about time travel and the future of humanity as well as segmentation of society into the haves (the Eloi) and the have-nots (the Morlocks). The Time Machine has been adapted to film many times.
• Flowers for Algernon, Daniel Keyes [link] [back-up link] 
  Classic story about modifying intelligence and the tragedy of technology; subsequently expanded to a novel and then a wide release movie. Very smart, well written, and moving.
• Who Goes There, Don A. Stuart (John W. Campbell) [link] [back-up link]
  Classic story about mutating aliens; a thriller/horror gem and meditation on identity. Brilliantly written, Who Goes There has been made into a movie multiple times with mixed results.
  
• The Library of Babel, Jorge Luis Borges [link] [back-up link] 
  Borges classic about a library, seemingly infinite, containing all possible books randomly stored, each 410 pages long, randomly composed in an alphabet of 23 characters. The books, of course, are mostly meaningless, but somewhere in there they also contain all truths, all fictions, all translations, all indexes ... at its core this is a mediation on people attempting to make sense of and cope with our Universe. 
• Universe, Robert Heinlein [no online text located] [mp3 radio adaptation]
  Classic short story of a "Generation spaceship" and a meditation on religion, society, and reality. Heinlein followed up with the story Common Sense 12 years later, which is mediocre and polemic, publishing it with Universe as Orphans of the Sky.
• Nightfall, Isaac Asimov [link] [back-up link] [mp3]
  Classic science fiction story about the clash between superstiton and science; this is the great science fiction writer's best stand alone story.
• Super Toys Last All Summer Long, Brian Aldiss [link] [back-up link]
  Classic very short story on the dilemma of machines possessing human feeling; badly expanded and made into the movie AI: Artificial Intelligence.
• It's a Good Life, Jerome Bixby [link] [back-up link]
  Classic short story about coping -- or not -- under the yoke of an arbitrary greater power.
• Born of Man and Woman, Richard Matheson [link] [back-up link]
  Classic "mutant child" science fiction story; very short and very moving.
• That Only a Mother, Judith Merril (Judith Josephine Grossman) [link] [back-up link]
  Not wanting to give anything away, let me only say this is a classic story about how our perception of reality changes as reality changes; this is also one of the few sf stories told primarily from the perspective of a woman.
• Jeffty is Five, Harlan Ellison [link]
  Voted the best science fiction short story of all time by Locus, Jeffty is Five is a classic story of a boy who never grows up and lives in a sort of bubble of a world that somehow does not age even as the rest of the world ages around it. It does not end ... well ... you'll have to read it.
• The Veldt, Ray Bradbury [link] [back-up link]
  Another classic story about children, here children whose family live in a house that does everything for them, but their parents want to leave ... 
• The Ones Who Walk Away From Omelas, Ursula K. LeGuin [link] [back-up link]
  LeGuin's classic about a "perfect" city, the price of which is that one child in the city must live in darkness and misery.  But for those who cannot accept this ...
• The Moon Moth, Jack Vance [link] [back-up link]
  A classic on culture and the clash of cultures, a murder mystery on another planet.
• Arena, Fredric Brown [link]
  The classic story of combat between a human and an alien, a common fantasy of geeky American boys; adapted, not so well, into a classic Star Trek episode.
• Twilight, John W. Campbell [link] [back-up link] [mp3]
  Classic story of a hitchhiker who happens to be from ... the future.
• The Midas Plague, Frederick Pohl [link]
  A tale about the need to consume; a classic if a bit over the top extrapolation on the economics of  a highly technological consumer society.
• The Marching Morons, C.M. Kornbluth [link] [back-up link]
  Classic story about the supposed dumbing down of society and stupid people taking over the Earth; loosely adapted into the movie Idiocracy. Read also The Little Black Bag (here an old tv adaptation), Kornbluth's superlative story about avarice and redemption for which The Marching Morons was a sequel.
• An Enemy of the People, Henrik Ibsen [link] [back-up link]
  Classic play (often read as a story) about the discovery of contamination of hot springs that are the source of a town's wealth. The citizenry refuses to address the problem, vilifying the scientist/discoverer of the contamination, and leaves themselves to the results. 
• Vintage Season, Lawrence O'Donnell (Henry Kuttner and Catherine Moore) [link]
  Classic story about the ethical dilemmas of time travel, though, admittedly, that may not seem to be what it's about at all. Very well written.
• Microcosmic God, Theodore Sturgeon [link] [back-up link]
  More of a classic fable in the form of a story, this tale involves artificial life, humans as gods over their creations; the tension between those who seek knowledge for its own good and those who seek it for power, and the consequences of not understanding what you control.
• The Lottery, Shirley Jackson [link] [movie part 1] [movie part 2]
  Classic very short story commingling aspects of an idyllic small town with brutality, religiosity, and arbitrariness; a model of building tension within a story.
• Scanners Live in Vain, Cordwainer Smith (Paul Linebarger) [link]
  Classic story about choice and purpose in life as well as the mode and ends of space travel.
• Mars is Heaven!, Ray Bradbury [link] [tv adaptation pt 1] [tv adaptation pt 2]
  Bradbury's classic tale of human arrogance and the frailty of emotion; the best story in his anthology/novel of short stories The Martian Chronicles (where it appears as The Third Expedition).
• A Martian Odyssey, Stanley Weinbaum [link] [back-up link]
  Classic story about non-carbon (silicate) life forms and the potential oddness of aliens. Dated but influential, it has a spirit never fully recaptured.
• Surface Tension, James Blish [link] [mp3]
  A classic meditation on anthropomorphism and biological possibility.
• The Nine Billion Names of God, Arthur C. Clarke [link] [back-up link]
  Classic story about technology and "God"; arguably Clarke's best short story.
• The Nose, Nikolai Gogol [link] [back-up link]
  Classic Russian tale of a civil servant's nose that departs from his face and starts to live a life of its own. Too absurdist for many American sf fans' tastses, but a classic (though more of fantasy than sf, admittedly). One might say this story is anti-scientific.
• The Cold Equations, Tom Godwin [link] [back-up link]
  Although Godwin did not originate the idea, this is the classic take on the ethical dilemma between a future chance to save multiple lives weighed against protecting one life now told here as a tense drama in space. The story behind this story is also interesting.
• They're Made Out of Meat, Terry Bisson [link] [back-up link] [video] [mp3]
  Classic very short story about aliens and anthropomorphism; an internet trope and fun read.
• Metamorphosis, Franz Kafka [link] [back-up link]
  Gregor Samsa turns into a cockroach. More fantasy than science fiction; a classic about the possible absurdity of the human circumstance.