"Sonny's Blues" by James Baldwin
"To Room Nineteen" by Doris Lessing
"Parker's Back," "A Good Man Is Hard to Find," or "Revelation" by Flannery O'Connor
"A Worn Path," "The Wide Net," "Why I Live at the P.O." and others by Eudora Welty
"The Garden Party" by Katherine Mansfield
"Flowering Judas"and "The Jilting of Granny Weatherall" by Katherine Anne Porter
"The Veldt" and "I Sing the Body Electric" by Ray Bradbury
"Rita Hayworth and the Shawshank Redemption" by Stephen King (technically a novella), and "Sometimes They come Back"
"Araby" by James Joyce
"Paul's Case" by Willa Cather
"The Lottery Ticket" by Chekhov
"Ransom of Red Chief" by O. Henry
"A Passion in the Desert" by Balzac

And many many more... I ADORE short fiction.