Yesterday, I posted Supergee's three books that changed his life, and Oz Fritz (in the comments) listed his three. After thinking about it for a day or so, here are mine:
1. ILLUMINATUS! Robert Shea and Robert Anton Wilson. There's obviously a lot that can be said about this book, but just one of the things I like about it is the philosophical agnosticism — none of the characters can ever be sure they are getting a real idea of what's going on. That's true even of the protagonists narrowly focused on solving a problem in their area of expertise, i.e., the New York City police detective trying to investigate a crime, a missing persons case that might be murder. Wilson remarked many years later (in Cosmic Trigger 3, Chapter 31) that "I see the universe as Puzzle to Work On, Joyce-Welles fashion, and not as Puzzle Solved," and that's one of the major themes of the trilogy.
Notice also that the "puzzle" of what kind of novel ILLUMINATUS! is can't really be solved. Is it a literary novel, or a pop culture novel? (How many readers notice right away that Hagbard Celine is sailing around on a yellow submarine, just like the Beatles song?) Is is a literary novel, a mystery, an occult-horror novel, a science fiction novel, a political novel a la Ayn Rand or a Cthulus Mythos novel? (H.P. Lovecraft even appears as a character in the book.) It would seem to be all of those things.
2. Pride and Prejudice, Jane Austen. I've always liked fiction that is "out there" — science fiction, ambitious literary fiction (I've liked Vladimir Nabokov since high school), complex books like ILLUMINATUS!
More than any other book, Pride and Prejudice taught me about the power of fiction that is straightforward, written in clear prose, about everyday people in the present doing ordinary things. I went on to read all of Austen's works, and I still read many "Austenite" comic novels about everyday people in the present (I've read everything by Tom Perrotta, for example, including his new one, and most of Elinor Lipman's books.)
3. The World of Late Antiquity, Peter Brown. This book, and Hugh Elton's Warfare in Roman Europe AD 350-425 helped focus my interest in late antiquity, a wonderfully interesting period in history which is neither classical history not medieval history, but something in between. At the same time that the Angles and Saxons were invading Britain and creating "England" — the putative time of King Arthur, in other words — the inhabitants of Constantinople, the new Rome, were still going to public baths and watching "Ben Hur" style chariot races.