Hmm. I don't think I've weighed in on this thread yet. Considering the amount of short stories I read, I really ought to. My favorites. Well, let's see, there are so many...
I suppose I ought to go through the list of books I've rated and do what clong did, and sort out short stories I've rated highly. Unfortunately, rather a daunting task, so I think it will have to wait until another day.
I've generally found that many authors who primarily write novels write poorly when they venture into short story form--mostly because a short story is not simply a short novel, or a piece of a novel, any more than a poem is a piece of prose broken up into lines.
Borges wrote almost exclusively short stories, some of which are truely mind-bending. "The Garden of Forking Paths", "The Babylon Lottery" "The Circular Ruins" and "Tlön, Uqbar, Orbis Tertius" are some of his best. Absolutely a must read for anyone who likes literary fantasy.
Franz Kafka,
Nikolai Gogol and
Italo Calvino are some other masters at the short form.
I recently discovered
Ilse Aichinger, an Austrian author who is likely to be unfamiliar to English-language readers, but who is worth looking up if you've liked the above-mentioned authors.
Isak Dinesen is pretty good too, and another author who wrote almost exclusively short stories.
Nathaniel Hawthorne is likely to seem a bit old-fashioned and preachy, but his best stories are definitely thought-provoking and worthwhile.
Others here have mentioned
Ursula K. Le Guin, and I would definitely agree. I first fell in love with her writing from her short story collections, and only later learned to appreciate her SF novels. "Changing Planes" is fun; I also liked "A Compass Rose" and "Orsinian Tales".
I like
Isaac Asimov, but I've found that his writing tends to be really good or really mediocre, and this is perhaps even more noticable in his short stories than in his novels. Some of his best (and most groundbreaking) are probably the stories collected in "Robot Dreams".
Both
Saki and
O. Henry are well-known for their short stories, although I confess I haven't read much by either.
Fairy tales (particularly literary fairy tales) are another favorite of mine, and an entire subject in themselves.