Joe Carter at the Confabulum has put together a short list of great short stories. He's got some good ones on there, but there are a few glaring omissions as well as some that I wouldn't expect anyone to think of, but that belong on any longer list of great short stories:
"The Whirligig of Life," O. Henry. How can one produce any list of short stories without the master of the genre?
"Pray Without Ceasing," Wendell Berry. Berry is still ignored on most short story lists; that won't last long. And, by the way, he has been churning out short stories over the last year or so, some of which have been published in various magazines and journals, all of which are now being collected for a new book.
"The Sire de Malatroit's Door," Robert Louis Stevenson. One of the few writers who could write a story about two strangers who fall in love over a two hour period and make it totally believable.
"Brothers are the Same," Beryl Markham. The author of the West With the Night also wrote several short stories which live up to the standard set by the book. This one is a masterpiece.
"Blackberry Winter," Robert Penn Warren. A haunting story by a great southern writer about the onset of the modern world.
"The Illiterate Spider," Billy C. Clark. The almost forgotten Kentucky author of The Song of the River was told when he went to the University of Kentucky (the only person in his town who ever went to college) by then department chair Guerney Norman (a great writer in his own right) that he was the best natural born story teller he had ever seen. Norman was right.
"The Bet," by Anton Chekhov. Another master of the genre.
"The Children's Story," by James Clavell. You'll never see this one anthologized because it was printed as a book--and made to appear like a children's book. The form in which is presented is essential to the presentation. It takes place over 23 minutes and shows how brainwashing can be accomplished subtlely and insidiously.
"The Lightening Rod Man," Herman Melville. A haunting evocative story.
"The Doomdorf Mystery," by Melville Davisson Post. Another masterpiece by a forgotten author.
"Barn Burning," William Faulkner. Faulkner. 'Nuff said.
And what about Washington Irving, Rudyard Kipling, Mark Twain, and Poe? These would have to be on any complete list. The short story doesn't get enough attention these days. Let's hope that changes.