All of these are books I recommend. I would also recommend reading all of the fiction here blindly, without knowing too much about it beforehand. The reviews are there if you need more convincing though.
Notes From Underground - Dostoevsky: Brilliant and disturbing psychologial insight, a classic.
Crime and Punishment - Dostoevsky: A dramatic look into the mind of a troubled and guilty man.
Stoner - John Williams: The deeply depressing and unfulfilling life of William Stoner.
Dune - Frank Herbert: Probably the best science fiction out there.
Invisible Cities - Calvino: 55 cities described meaningfully.
Lord of the Flies - Golding: An exhibition of the savagery that's dormant within all of us.
The Death of Ivan Ilych - Tolstoy: The slow, emotional, and insightful death of an average man.
The Picture of Dorian Gray - Wilde: The Faust legend retold in very good victorian british writing.
Human Smoke - Nicholson Baker: World War 2 History with a twist.
Meditations - Marcus Aurelius: A classic in self help and stoic philosophy.
Metaphysics of War - Evola: Analyzing the spiritually fulfilling nature of war.
The Origin of Language - Gans: A linguistic theory that turns into a theory of everything.
Anthropomorphics - Bouvard: The best insights offered by Generative Anthropology.
Crisis of the Modern World - Guenon: A spot-on metaphysical diagnosis of our declining society.
Nemesis - C.A. Bond: Illiberal political theory based on Jouvenel's analysis of power.