So many stories. Here are a few (mostly SF) favorites of mine that may not have been discovered by some:

"Allamagoosa" by Eric Frank Russell (this marvelous story won a Hugo for best SF short story of 1955)

"The Ghost Ship" by Richard Middleton (dating from 1912, this is my favorite story for reading aloud and it's available free online -- here, for example)

"They're Made Out of Meat" by Terry Bisson (another SF story -- a short short this time -- also available free online here)

"Noise" by Jack Vance (a wonderfully atmospheric, loooong SF story from 1951 that hasa been anthologized several times)