Neat idea...I haven't read too many SF short stories, but I'll nominate some that I've loved...
The Fifth Head of Cerberus : Gene Wolfe -- Later used as part of a three part novel, this story of a boy scientist who may be a clone growing up in a decrepit whorehouse on a planet modeled after Rimbaud's North Africa is probably my favorite short story ever...yes, better than "Araby"...
Every other Gene Wolfe story ever -- I'm a nerd.
Johnny Mnemonic: William Gibson-- Just a little bit better than the film. OK a lot better.
A Little Something For Us Tempunauts -- Philip K Dick...good description on this
wiki
Repent, Harlequin!" Said the Ticktockman -- Harlan Ellison
Even less science fictiony:
The Brave Little Toaster - Tom Disch (You heard me!)