Name: Escape from New York
Written in: 1981
Set in: 1998
Why it's a dystopia: The country has a federal police service AND has turned Manhattan into a maximum security prison. Worse, the Soviet Union's still around.
Why it's significant: Snake Plissken is an iconic character; plus, the shock visuals that resulted from juxtiposing familiar American icons and an aura of decay had an impact on subsequent dystopian cinema. Which is a slightly pretentious way of saying 'people liked the film.'
What happened? Well, obviously, we didn't create a federal police agency of this sort, and we didn't make Manhattan into a maximum security prison. But that's not why I'm noting this: after all, Carpenter's somewhat jaundiced worldview about contemporary American societal trends can be seen more pointedly in his sequel Escape from L.A.* No, the reason I'm pointing this one out is because we're all getting older, which means that the population is increasingly one that has no real memory of what it was like to have the Soviet Union looming over us. The casual assumption that the USSR would be around and kicking in the next generation was utterly unremarkable at the time - which, given what we know about the nature of Marxists, implies some pretty dark deeds, in... deed.
Indeed, this is one of the more hopeful assumptions. Far too much science fiction of the time period assumed that the Soviets were going to end up kicking our butts.
*A movie which is notable partially for that, but mostly for being an egregious piece of sh*t whenever Bruce Campbell wasn't on the screen.