Okay, I'm not really into post-apocalyptic games in general. For me it is a very depressing genre. The term "post-apocalyptic" conjures up visions of ignorant, violent tribal a-holes fighting it out to see who gets to be King of the Trashpile. And you get to play one of those a-holes with a crappy present leading to an even crappier future. Might as well just jump off a bridge and get it over with.
On the other hand, the term "post-apocalyptic" actually covers a lot of sub-genres which are quite different. So for today's question I would say Gamma World, or Paranoia if that counts. I played Gamma World a long, long time ago, back around when it first came out. It was weird and wacky (not my usual style) but as long as I approached it as a silly game with silly random mutant characters it was fun. One game which I haven't tried but which sounds very, very cool is Tribe 8 by Dream Pod 9. I'm not sure my group would go for it, so I may never get to play it. But it's one of those games where I'll probably collect most of the books just to read all the cool stuff.