The Sword of the Spirits trilogy, starting with The Prince in Waiting - and several more by John Christopher
…and lots more
The Book of Dave by Will Self.
Although you may find some parts a challenge if you’re not familiar with (British) English vernacular.
Walter Tevis’s Mockingbird is a masterpiece by one of the best prose stylists to write any science fiction. His other works include The Hustler, The Color of Money, Queen’s Gambit and The Man Who Fell to Earth..
Can’t forget Brave New World or Harrison Bergeron. I’m not terribly fond of dystopian works myself, since I tend to find them oppressively gloomy.
There’s a wide-ranging list on TV Tropes (for your question, look in the Literature folder).
I loved Earth Abides, really interesting look at a pandemic, written right after WWII; instead of focusing on chaos it focuses on society devolving.
The Handmaids Tale
I saw that someone posted Oryx and Crake. I agree! This is actually part of a trilogy. After that was “The Year of the Flood”, then “MaddAddam.”
All by Margaret Atwood.
Ooh, surprised I get to be the first to mention Cormac McCarthy’s ‘The Road’- that’s about as dystopian as it gets.
A Clockwork Orange.
James Ellroys LA quartet…The Black Dahlia, The Big Nowhere, LA Confidential and White Jazz.
Count Zero, Neuromancer by William Gibson.
I’m finding it hard to find science fiction that ISN’T dystopian. I find it gloomy, too.
Seconded. All the dystopian stuff decades before the form became popular, by someone who fled early Communist Russia and knew a dystopia first hand.
California by Edan Lepucki
The Water Knife by Paolo Buciagalupi
Ready Player One. Read it before it becomes a movie in 2017!
I liked it, but it also contains some laughably vintage notions of women and African Americans.
Nevil Shute’s On the Beach. It’s a bit dated but scared the crap out of people in its time. Also Robert Neville’s I Am Legend, which is very depressing.