One of the brilliant things about A Clockwork Orange is that it has its feet in four different genres: dystopian novel, coming-of-age story, horror flick, and political satire.
From the top: it's a dystopian novel because it takes place in the future, and everything is dark, eerie, violent, and headed down a dismal and non-utopian path. It's a coming-of-age story because of the trials and transformation Alex endures. The horror aspect of the work is pretty evident: check out all the beating, teeth-plucking, eye-gouging, mugging, and raping that occurs. The satiric aspect comes through in the novel's political commentary. Finally, amidst all that debate about moral choice, free will, personal freedom, and behavioral modification, Burgess conveys a real anti-totalitarian message in this novel.