Oooh...tough one, as I do love so many. If I had to just pick one though, it would be "Nineteen Eighty-Four". For some reason, this movie and book just resonates with me. It's hard to say exactly why, but it just does. Granted, I do love dystopian future movies and this is definitely one of the bleakest I've seen. Something about it just pops with me, and I love it.
Other honorable mentions...
Clockwork Orange: Almost forgot about this one, but like Ninteen Eighty-Four this is a great piece of dystopian, low-level sci-fi. Maybe because the two are about what makes up humanity, or perhaps because in many ways they are in the realm of close possibility compared to many other sci-fi movies. At any rate, decent movie.
A Boy and his Dog: A cult classic. One of the big influences for one of my favourite game series, Fallout, this is a good movie, and I love the chemistry between the main character Vic and his dog Blood. I admit, I like the first half of the movie a lot more then the second half, but still, it's one of my favourites.
The Road: Yeah, depressing as fuck, but still, I enjoyed this movie, and when feeling in a dystopian mood, this is a movie I sometimes pop in.
Blade Runner: How could this not be in here? Cyberpunk meets Film noir. A classic bit of sci-fi, which made a lot of people think, and had a great deal of eye candy. They did an amazing job of bringing the world of Blade Runner to life, and I'd be lying if I said I wasn't looking forward to seeing what they plan to do next for the sequel.
The Matrix: Personally, I enjoyed all three movies, but even if you just liked the first one, it was still a great movie that seemed to open up movies to the next level of action sequences.
Johnny Mnemonic : I know, not exactly a great movie, but for somebody who was just getting into cyberpunk like Shadowrun, this movie was great. It was easy to see how the two overlapped, and is still a favourite to this day.