My answer below; answers from other people here.
Any book worth its salt should be able to withstand a second reading, but there are some that excite and move me at every reencounter. Here are a few:
Concrete Island by J.G. Ballard. A man finds himself stranded on a traffic island after a car crash. At first he can’t escape. And then he doesn’t want to. A powerful, deceptively simple updating of the Robinson Crusoe story.
Dhalgren by Samuel R. Delany. A man comes to a wounded American city, leaves as a hero-poet. After the fall of New Orleans, it’s more relevant than ever.
Libra by Don DeLillo. Oswald as tragic hero.
Neuromancer by William Gibson. Still fresh and startlingly original, despite a thousand imitators.
The Inheritors by William Golding. Neanderthals encounter modern humans, with fatal results. All of Golding is worth reading and rereading, but this is my favourite.
Climbers by M. John Harrison. A beautifully written, intricately structured memoir/novel about memory, obsession, and the unrelenting reality of the world.
The Dispossessed by Ursula K. LeGuin. Diagrammatic, yes, but the sections set on Anarres are truly powerful and moving, and it’s one of the few SF novels to attempt to portray a genuinely original society from the inside.
Child of God by Cormac McCarthy. America primeval.
Picnic on Paradise by Joanna Russ. Alyx, a barbarian kidnapped by the future, leads a gang of squabbling tourists across an alien wilderness. Alyx is the template for every wisecracking kickass heroine in cyberpunk, the new space opera and much else, but she’s the original and best, tough and funny and tender and wise.
Rabbit, Run, Rabbit Redux, Rabbit is Rich, Rabbit at Rest by John Updike. The detailed life and times of Updike’s American Everyman are, like America itself, inexhaustible.
The Once and Future King by T.H. White. A marvellously eccentric fantasy about King Arthur, the Round Table, and the Matter of Britain that begins as a juvenile comedy and ends in tragedy and renewal. The death of Beaumont gets me every time. And no one does infodumps like White, who seems to know everything about Medieval Britain, which he remakes into a world that never was but should have been.
Random Acts of Senseless Violence by Jack Womack. The fall of America, as told to her diary by a young girl. The best, and chronologically the first, of Womack’s Ambient sequence.
So, which books do you recommend?