Unfortunately not much.
From ANALOG, Stan Schmidt collected a few shining examples of humorous SF in ANALOG’S LIGHTER SIDE and BEST OF collections – most notably “The Dread Tomato Addiction”, though it wasn’t strictly a short story and it turned on the idea that you can make statistics say whatever you want them to say. Written by Mark Clifton, it was published in ASTOUNDING in 1958, and when I read it for the first time in left a deep impression on me.
Kelvin Throop was the star of several ANALOG short stories in the 1960s through the 80s and had numerous sayings attributed to him. Invented by R.A.J Phillips, several writers wrote stories about him and he became a sort of fall back for snarky sayings that were space fillers.
The website BestScienceFictionStories.com has 78 stories that they consider “Funny” – http://bestsciencefictionstories.com/category/funny/. I just discovered it when I started looking for humorous SF. Other recent forays into speculative short fiction humor come from a writer I first came across in an online writer’s group I’m a member of, CODEX’s Alex Schvartsman. The third UNIDENTIFIED FUNNY OBJECTS anthology is due out later this year and I’ve got a story I may submit there.
So I KNOW humorous short stuff is being written – but it doesn’t seem that there are many writers who have become closely associated with it any more. Gordon R Dickson and Poul Anderson wrote the Hokas series, Asimov’s sporadic funny stuff, even Haldeman wrote “A !Tangled Web”, Mike Resnick – but no one seems to have emerged as a regularly humorous writer – and it seems “everyone” has written funny short stories as evidenced by Resnick’s THIS IS MY FUNNIEST: SCIENCE FICTION WRITERS PRESENT THEIR FUNNIEST STORIES EVER volume one and two.
Yet it doesn’t seem that the awards come to humor. An old friend of mine who is a prolific writer of YA humor has never once been up for a Nebula, a Hugo, a Newbery, a Printz, Morris, Globe-Horn, or ALA Best...because none of the committees believe that serious issues can be dealt with humorously.
I think that this may also be the problem with speculative short fiction as well. When it comes time for the awards to be handed out, people say to themselves, “Wow! That was funny! But serious can’t be funny, so I’d better not nominate/vote for/write something funny because no one will take me seriously.”
Of course, we need only look at the accolades showered on the King of Television Dramedy, M*A*S*H: 12 Emmys, a Golden Globe, a Peabody, a Director’s Guild of America, several Humanitas Prize and Writers Guild of America nominations, an exhibit in the Smithsonian, and one of the highest ratings in the history of the Neilson’s for its final episode.So where is science fiction’s short fiction version of M*A*S*H, O. Henry, or James Thurber, eh?