I will say straight away, the main reason why I like dystopian stories is because I like new things. I get bored of the same thing over and over again. This applies to both books and movies, although it usually happens more frequently on the latter.
Even when you read two dystopian novels with a similar concept or hero portrayal, the world tends to change. That change stimulates my creativity and it makes me wonder, who would I be in that world?, what kind of problems would those people face beyond what's written?, how did society get to that point?, what would happen a hundred years after the events in the story?
They make me think, and I like thinking. A lot.
Dystopian stories happen in the future, or at least in a future from the moment it was written (as it happens in '1984'), and I love futuristic stories: with and without sci fi. If you tell me a story is set in the future, there is a 75% chance I will read it. The rest depends on many other factors, but you get the idea.
Young adult dystopias have been very popular recently, leading to many people reading and writing on the subject. Although this is great because it makes people read and think, here's the sad part. Authors have been writing dystopias long before yesterday, long before the internet and even television. A lot of people who call themselves "fans of dystopian stories" nowadays, haven't read any of them. They might not all be Young Adult material, but they are far beyond comparison. The research, the ideas, the characters, the message.
To conclude this post, here are some of my favorite non YA dystopias that are a must read for anyone: '1984' by George Orwell, 'Anthem' by Ayn Rand, 'Fahrenheit 451' by Ray Bradbury, and 'Brave New World' by Aldous Huxley.
Not into books? Watch 'Gattaca', 'V for Vendetta', 'Equilibrium', 'Blade Runner', 'The Matrix', and 'The Island'.