These are most of history's classic short stories that are currently online and in English, along with their links.
Big thanks to Project Gutenberg and The Library of Short Stories for most of these links.
Literary
#1 The Lottery by Shirley Jackson
#2 The Yellow Wallpaper by Charlotte Perkins Gilman
#3 Metamorphosis by Franz Kafka
Hills Like White Elephants by Ernest Hemmingway
An Occurrence at Owl Creek Bridge by Ambrose Bierce
The Lady with the Dog by Anton Chekhov
To Build a Fire by Jack London
Miss Brill by Katherine Mansfield
The Gift of the Magi by O. Henry
The Necklace by Guy de Maupassant
Sci Fi
#1 The Last Question by Isaac Asimov
#2 A Sound of Thunder by Ray Bradbury
#3 Harrison Bergeren by Kurt Vonnegut Jr.
The Nothing Equation by Tom Godwin
The Coming of the Ice by G. Peyton Wertenbaker
No Moving Parts by Murray F. Yaco
Gothic/Horror
#1 A Good Man is Hard to Find by Flannery O'Connor
#2 The Call of Cthulhu by H. P. Lovecraft
#3 The Tell-Tale Heart by Edgar Allan Poe
The Cask of Amontillado by Edgar Allan Poe
The Masque of the Red Death by Edgar Allan Poe
The Monkey’s Paw by W. W. Jacobs