Hey - I think it's in the handbook somewhere that I reply to this (I'm an English grad. student). So hurrah for posting it, Laurie!
Actually, a professor of mine had an entire class devoted to dystopian future lit. about a year ago - her three core books were Dr. Bloodmoney by Dick, Cat's Cradle by Vonnegut, and The Sheep Look Up by John Brunner (KharBevNor mentioned another of his books - Shockwave Rider).
I didn't get a chance to take the course, but she lent me a syllabus; I've read Dick's and Brunner's books. If you want a recommendation, absolutely you must read The Sheep Look Up. It's not your classic dystopian novel - first, it's postmodern, so the story unrolls from dozens of perspectives all at once, brilliantly handled. Second, it's centered on ecological problems, like insects and vermin becoming immune to our poisons and a toxic food supply. It's very scary, if you look at modern ecological motions in American government (it's set in the United States).
Also, I've yet to read (but have a copy and eagerly await it to come up in queue) A Canticle for Leibowitz, but the strange fetishizing of technology after an apocalypse (it becomes a religion after it's forgotten) has made it famous as well.
Laurie, you mentioned a book written in the nineteenth century? Were you talking about More's Utopia? We discussed that a bit in theory class (as well as 1984, Brave New World, and Blade Runner/"Do Androids Dream of Electric Sheep?"), and I think the prevalent idea is that it's a parody - that is, More probably didn't feel a Uptopia was possible, and the book was his attempt to illustrate what would happen if we tried for one. The classic dystopian books (again, 1984, et cetera) follow this pattern - most characters believe the world is a utopia. The more recent dystopia novels don't do that; it's generally thought of as a reflection of our move away from the Enlightenment/Romantic idealism and toward the post-war cynicism.
Also, Huxley wrote a companion to Brave New World called "Braver New World," a non-fiction piece about how society decades after the novel's writing did and didn't match what he'd foreseen.[/u]
A few people have mentioned cyberpunk - good for them! I'm a huge cyberpunk fan. Stephenson actually wrote a semi-dystopian book (apart from all the others of his mentioned so far) called Zodiac. It's about ecology as well, and isn't as far-reaching as most dystopias, but it does deal with the private sector's influence on that sort of problem.
If you really want some hard-hitting pieces of cyberpunk (almost all the traditional cyberpunk could be considered dystopian, though the government isn't always a huge conspiracy) check out William Gibson's collection of short stories, Burning Chrome.
Of course, one could also consider sections of Wells' The Time Machine - the society that spawned the Morlocks is certainly a poor place to consider as our future.
And I thought I would mention my personal favorite - Moorcock's Cornelius stories, particularly The Final Programme. It's easiest to find this book in a collection called The Cornelius Quartet. The other three books follow the same line, in a sense, but they're also grand experiments in the New Worlds sixties style (New Worlds magazine was edited my Moorcock in the sixties), so they also run ragged into a lot of other ideas. The Final Programme features a London empty of people and full of a mob that functions as a hive mind (adapted to survive the blow to individuality that the end-times is), and a kind of computer mind-dump golem devouring all things. Some people cite Jerry (Cornelius) as the first cyberpunk hero, though that's debatable.
Jeez. Okay, I actually haven't posted over in the "I'm new" forum yet, so this is my first post. I couldn't resist the allure of literature.