Hitchhiker’s Guide to the Galaxy may count. Begins with the end of the world.
Seeking a Friend for the End of the World is an upcoming comedy about an Asteroid hitting the earth.
Looks very funny.
Arguably Don Johnson’s best work.
Just a short essay, only a few pages, but a seriously funny classic – available online in several formats:
A Modest Proposal by Jonathan Swift
What, no love for Woody Allen’s Sleeper?
I own this but have not yet read it, though I have heard that it’s quite funny. I should get around to reading it one of these days: Sewer, Gas and Electric
Any society with a young Diane Keaton and an Orgasmatron is a utopia, not a dystopia.
So true! I tried watching it on Netflix recently and it was not good at all.
Not a dystopia, per se, but the kid’s show Adventure Time takes place 1000 years or so after a nuclear war. The war is still relevant since there are characters that were alive during the actual war (magic happened, so there are immortal beings and such). It’s otherwise light and happy, but there are definitely hints of something darker in the background.
Way back in the Dark Ages…the 70’s…we played RPG games. I eneded up refereeing most of the time because, frankly, I was damn good at it 
There was one friend who sucked…SUCKED at refereeing and he so wanted to do it. The problem is that he always started to take things as a competition and would go against the players…a terrible characteristic in a referee. He also was an extremely cynical/depressed person.
Except Paranoia. He was an EXCELLENT Paranoia referee. I still laugh at some of the things that happened when playing it.
I would think Max Headroom deserves a mention. Man I loved that show.
The French movie Delicatessen is both funny and dramatic, and is about a not-quite-apocalyptic but unspecified-disaster-stricken world (near famine is the main plot point).
Jasper Fforde of Eyre Affair fame had a new book out a bit ago, Shades of Grey, which seems to be first of a series. It’s a far-future post-apocalyptic dystopia where one’s social class is determined by how many colors one can see. Very funny if you like that sort of thing.