Set in: 1999
Why it's a dystopia: Overcrowding. The population of NYC is over 35 million (USA population around 350 million; world population is - oh, my GOD! - seven billion); the planet is more or less incapable of feeding itself; and there's not enough power or resources to go around. As in, there's pretty much no power grid.
Why it's significant: In 1973 They turned this book into Soylent Green.
What happened? Well, essentially the Green Revolution - much to the chagrin of Paul Erhlich, who has been forecasting the collapse of civilization for longer than I have been alive, and getting away with never getting it right, either. Turns out that you maybe shouldn't let entomologists practice math without a license: fortunately for the Third World - and especially India - we had people like Norman Borlaug, savior of one billion people and (as per blogger Iowahawk's magnificent brag) the greatest Iowa farmer who ever lived. It also turns out that richer societies can get their population under control without the need of Ehrlich's rather draconian methods.
Anyway, it turns out that we can have a population of about 250 million people in the USA in 2000 without needing to have a NYC of more than about 8 million or so - and NYC was pretty darn spiffy back then, thanks largely to Rudy Giuliani. Say what you like about gentifying Times Square, but it was nice to be able to walk through it without getting solicited by pimps every fifteen feet. And the lights are on!