...continuing my year-end listmania:
Lucian, "True Histories" (in Penguin Classics volume Chattering Courtesans and Other Sardonic Sketches). Ancient Roman source for Baron Munchhausen tales, Terry Gilliam's film, and much else in Western comic / satirical / fantastical writing.
Boccaccio, The Decameron. One of the greatest (and funniest) collections of short fiction ever written. There are so many good tales here that I can't possibly choose just one.
"The Fall of the House of Usher" by Edgar Allan Poe. The best Poe is the weirdest Poe, the Poe that will never go out of style.
"Bartleby the Scrivener" by Herman Melville. For me, one of the defining works of the American short story tradition (to the extent that such a thing exists).
"The Figure in the Carpet" by Henry James. It is wondrous to watch old Henry weave and try to guess what warps his woof.
"Ward Number Six" by Anton Chekhov. Hard to choose a single Chekhov story (and there are many I haven't read), but this one is exceptional.
Three Tales by Gustave Flaubert. Again, can't choose one, so why choose? Read all three; they're short and great. Smutty secret: the French title, Trois Contes, puns for "Three Cunts." Think about that after you've read the book.
"Counterparts" by James Joyce. One of the best and darkest stories in Dubliners.
"Tlon, Uqbar, Orbis Tertius" by Jorge Luis Borges. Really everything is Borges's Collected Fictions in marvelous, and the book is an essential part of any library (because it contains every library, and all books).
"A Clean, Well-Lighted Place" by Ernest Hemingway. Perfect.
"The Death of Justina" by John Cheever. One of the greatest American short stories, period. This is Cheever at his most original and most Kafkaesque; after reading this, you won't need to read Don DeLillo, because much of DeLillo's America is anticipated here. If you think you know Cheever but you haven't read this, you don't know Jack about Cheever.
"A Rose for Emily" by William Faulkner. There's something about the narrative voice here that grabs me at the opening phrase and doesn't let go.
"In The Penal Colony" by Franz Kafka. Every time I read it, it's a different story, and every reading seems the first.
"The Terminal Beach" by J. G. Ballard. Everything in The Best Short Stories of J.G. Ballard is worth reading.
"Good Country People" by Flannery O'Connor. Yeah, the title's ironic. Very, very ironic.
"A Small, Good Thing" by Raymond Carver. Minimalism has gone to its cemetery of blank tombstones, but Carver's stories remain, as easy as talking and harder than rock.
"Scale" by Will Self. Self at his outrageous, surreal, satirical best. Laugh-aloud funny and constantly surprising.
"Brief Interviews with Hideous Men" by David Foster Wallace. This novella, broken into story-length fragments in the eponymous book, is a great example of Wallace doing what he does best, voices.
"Helping" by Robert Stone (in his excellent collection Bear and His Daughter). Easily one of the best American short stories of the twentieth century.
"Brokeback Mountain" by Annie Proulx. Read Annie Proulx's Wyoming stories. Read 'em all, in three volumes. They contain some of the finest prose written by anyone still on the upright side of the American sod. She is one tough broad.