Only one??!! Hoo, boy ... Okay. I'll try.
"Homecoming" by Ray Bradbury -- I would nominate this as one of the great, if not the greatest, American fantasy short story of the 20th century. It takes the tropes of the horror story and makes a very human statement about love and loss, about being an outsider and also about family. (If I didn't choose this, I'd probably go with Fritz Leiber's "Smoke Ghost".)
And there are so many great collections:
The Martian Chronicles and The October Country by Ray Bradbury
Good Neighbors and Other Strangers and Still I Persist in Wondering by Edgar Pangborn
The Collected Stories of Ernest Hemingway
Collected Stories by Raymond Chandler
The Selected Stories of Ring Lardner
12 Stories by Frank O' Connor
The Two Sams by Glen Hirshberg
The Adventures of Sherlock Holmes by Sir Arthur Conan Doyle
Night's Black Agents & You're All Alone by Fritz Leiber
The Bloody Chamber and Other Stories & Burning Your Boats by Angela Carter
Bloodchild and Other Stories by Octavia Butler
None So Brave by Joe Haldeman
Extremities by Kathe Koja
Zothique by Clark Ashton Smith
The Throne of Bones by Brian MacNaughton
The Collected Stories of William Faulkner
The Collected Stories of Elizabeth Bowen
Seven Men by Max Beerbohm
The Continental Op & The Big Knockover by Dashiell Hammett
Randy M.