I would have to kindly agree with many people who already posted. Rather than suggesting stories (the list would extend beyond my attention span :p), I will suggest authors instead, in no special order, of course: O. Henry, Mark Twain, D.H. Lawrence, Oscar Wilde, Guy de Maupassant, Henry James, Flannery O'Connor, J.D. Salinger (especially his Nine Stories), Ernest Hemingway, Amy Tan, Franz Kafa, Edgar Allan Poe, Ambrose Bierce, Henry David Thoreau, Leo Tolstoy, and Zora Neale Hurston.
Additionally, I would like to add Fyodor Dostoevksy, but have yet to read any of his short stories, focusing more on his novels. Nonetheless, finding his novels enthralling, to say the least, as he lists among some of my favorite authors, I have no doubt in the superiority of his short stories, too. ;)
Happy reading!
