I once did some research to determine what were the most frequently anthologized short stories. This list can't be regarded as definitive, because, of course, I couldn't examine every anthology that's ever been published, but I did examine a lot of them. And my list is probably slanted toward American short stories, because that's where I did my research. And it may be a bit out of date, since I did the research maybe 20 years ago. Anyway, here's what I came up with:

All of these stories appear in at least 5 anthologies:

Sherwood Anderson, "The Egg"
James Baldwin, "Sonny's Blues"
Ambrose Bierce, "An Occurrence at Owl Creek Bridge"
Willa Cather, "Paul's Case"
Joseph Conrad, "Heart of Darkness" [some would classify this as a novel, but it does appear in anthologies]
Stephen Crane, "The Blue Hotel"
Stephen Crane, "The Bride Comes to Yellow Sky"
Stephen Crane, "The Open Boat"
Ralph Ellison, "Battle Royal" [which I think is actually an excerpt from his novel, "Invisible Man", but it stands on its own]
Ralph Ellison, "King of the Bingo Game" [ditto?]
William Faulkner, "A Rose for Emily"
William Faulkner, "Barn Burning"
William Faulkner, "That Evening Sun"
F. Scott Fitzgerald, "Babylon Revisited"
Charlotte Perkins Gilman, "The Yellow Wallpaper"
Nathaniel Hawthorne, "My Kinsman, Major Molineux"
Nathaniel Hawthorne, "The Minister's Black Veil"
Nathaniel Hawthorne, "Young Goodman Brown"
Ernest Hemingway, "Hills Like White Elephants"
Shirley Jackson, "The Lottery"
Henry James, "The Beast in the Jungle"
Henry James, "The Real Thing"
Sarah Orne Jewett, "A White Heron"
James Joyce, "A Little Cloud"
James Joyce, "Araby"
James Joyce, "The Dead"
Franz Kafka, "A Hunger Artist"
D. H. Lawrence, "The Horse-Dealer's Daughter"
D. H. Lawrence, "The Rocking-Horse Winner"
Jack London, "To Build a Fire"
Herman Melville, "Bartleby the Scrivener"
Flannery O'Connor, "A Good Man is Hard to Find"
Flannery O'Connor, "Everything that Rises Must Converge"
Joyce Carol Oates, "Where Are You Going, Where Have You Been?"
Grace Paley, "A Conversation with My Father"
Edgar Allen Poe, "The Cask of Amontillado"
Edgar Allen Poe, "The Fall of the House of Usher"
Katherine Anne Porter, "Flowering Judas"
Katherine Anne Porter, "The Jilting of Granny Weatherall"
John Steinbeck, "The Chrysanthemums"
James Thurber, "The Catbird Seat"
Leo Tolstoy, "The Death of Ivan Ilych"
Mark Twain, "The Notorious* Jumping Frog of Calaveras County" [* Some versions have "Celebrated"]
John Updike, "A & P"
Eudora Welty, "Why I Live at the P. O."
Richard Wright, "The Man Who Was Almost a Man"