Well, for collections, I’d reccommend Black Projects, White Knights, by Kage Baker, whom I absolutely adore.
Also, William Gibson’s Burning Chrome. There’s also an anthology of short stories called Mirrorshades edited by Bruce Sterling. I really love the story Mozart in Mirrorshades, but I don’t remember who it’s by, and since the book’s out of print right now, I have no way of checking (though I suppose I could bug the SO about it tomorrow since he owns it).
There was also this one anthology called Future Net that was pretty okay, if you’re bored, but I think you’d like it :).
Quite possibly because Clarke has a very similarly named story called “Who’s There?”, which I think can be found in the collection The Other Side of the Sky. I would also like to second those who have mentioned “The Nine Billion Names of God”. One of the best SF short stories ever.
I quite enjoyed the Callahan’s short stories by Spider Robinson - They were gathered in Calahan’s Crosstime Saloon and its sequals.
Lessee…
Off the top of my head - I always enjoyed Asimov’s Robot stories, found in I Robot, although they are not to everyone’s tastes - some have found that they’ve become too dated, though I disagree.
Heinlien has a few good ones, although I usually prefered his novels to his short stories. “The Long Watch” is one that comes to mind as a good one.
Ah, thanks Politzania for reminding me of that one - I remember thinking of it as the definitive “time travel paradox” story, done well and with humor that’s not entirely characteristic for Heinlein (at least in my limited experience with his rocket-ship-engineers-carrying-slide-rules “hard” SF tales).