"The Legend of Sleepy Hollow"
Visit the real Sleepy Hollow.
"Rip Van Winkle"
"The Monkey's Paw"
"An Occurrence at Owl Creek Bridge"
"A Spectral Collie" (not a great, but everyone knows I'm a Lassie fan...)
This is really suspense, not spooky, but it's my favorite short story along with "The Secret Life of Walter Mitty": "The Most Dangerous Game"
Incidentally, the site all these stories are on, Classic Reader.com, has a super selection of older short stories and books, including more stories by H.H. Munro ("Saki"), whom I love.