Bukowski, Dick, Chekhov, Kafka, Vonnegut, Greene, Hemingway, Twain, Joyce, Beckett, Hesse.
I'm missing a few dead Russians, sure.
Well, my reaction was a bit impetous, I admit. Although I consider some of those writers novelists, and not strictly short story writers. Poe was one of the earliest modern short story writers though, along with Maupassant. If we are looking strictly at American's, I'd still say he is at the top of the list. It's all opinion anyways, I'm not debating it because they are all great.
Bulgakov and Doestevsky for Russians.