Name: Car Wars, by Steve Jackson Games
Type: Board/Roleplaying Game (armored and armed car warfare on the dystopian highways of a future America).
Written in: 1980, to begin with; there have been multiple supplements since. 1996 is the publication date of the latest roleplaying supplement (GURPS Autoduel).
Set in: 2030-2046; I'm doing this one because according to the official timeline Rounds One and Two of Everything Turns To Crap were supposed to have happened by now.
Why it's a dystopia: For our purposes? Well, at this point the country's supposed to have lost Texas, Oklahoma, and Louisiana in a civil war; legalized blood sports; watched the environment go Full Metal Ehrlich; and suffered through a decade of domestic terrorism. And this is the part of the timeline that the future inhabitants are going to be nostalgic about.
Why it's significant: Honestly? Much as I love this game - and I do, I do - I'm doing it because it's a handy referent to peak oil in popular culture.
What happened? Well, the environmental estimates were as accurate as they always were - for some reason, radical Greenies really do tend to forget that rich people breathe oxygen, drink water, and metabolize organic material, too - but it's the peak oil thing that is probably the tell, here.