I would like to fourth My Old Man by Ernest Hemingway and third The Complete Stories by Flannery O'Connor .

Using my final nomination I will offer Fifty-One Tales by Lord Dunsany (Edward John Moreton Drax Plunkett, 18th Baron of Dunsany ). To me this collection shows Dunsany to be a master of the short story from pure fantasy to commentary on the human spirit and society. This collection is available in nice versions (LRF, PRC, IMP) here at MR, and being in the public domain for free at the other expected sources. This link (to one of the LRF versions at MR) provides more information as well as and example of one of his very short pieces.