* Neutrino Overdrive — One day in the 1950s, in the desert of California where the drag racers line up facing the Christmas lights, a new challenger appears. He is tall with a large forehead and olive colored skin. He wants to race.
* Breakfast at Tiffany's — technically a novella, but reads really fast. Different than the movie and better (in my opinion)
* Flowers for Algernon — One of the classics
* Country of the Blind — in the country of the blind, the one eyed man is king
* The Last Question — this is reposted so much on HN and Reddit that if you haven't seen it, yet, just wait a week :)
* The Blue Afternoon That Lasted Forever — Just wow. Actually a lot of the stories in Carbide Tipped Pens are really good. It is a good collection.
* The Nostalgianauts — It is easier to find this in audio than as a short story. It is in some collection somewhere
Maybe is not the most emotive (Tolkien's Leaf by Niggle and Ted Chiang's Story of your life are superior in that) or the most far into the future one (Asimov's The last question should be required reading), nor even the funniest one (hard pick, Asimov's The endochronic properties of resublimated thiotimoline fits there, if even because the story behind). But not is a so bad option.
If novellas are permitted (and somebody else included one), the "Hadji Murad" by Tolstoy has to be on the list.
He woke up to the sound of screams "Daddy!! Daddy!!". Fearing the worst he ran to his son's bedroom. He saw his son crying in the light from the open door. He rushed over to soothe him. The boy said "Daddy there's a ghost under by bed.". "There are no such things as ghosts", he said standing up."Here I'll show you", he said bending down to peek under the bed. He saw his son under the bed and the boy said "Daddy there's a ghost on my bed."
Haven't found any mystery short stories that are better than Sherlock Holmes. Labours of Hercules was good though.
My all time favourite: The Bet by Anton Chekov
http://www.gutenberg.org/files/1732/1732-h/1732-h.htm#link2H...