Following Tyler Cowen, a list off the top of my head of the 10 books that have most influenced me, more or less in the order I encountered them.
(I'm sticking to non-fiction because I have much more often done lists of top-ten favorite novels, many of which may well have influenced me as much or more deeply as any of the books on this list.)
1. Anthony Burgess, 99 Novels. A book that sent me, at age 15 or so, to read the 99 novels that Burgess (highly idiosyncratically) deemed the best published in English since 1945, thus introducing me to Pynchon, Ballard and a host of others.
2. Paul Fussell, The Great War and Modern Memory. I can't remember who recommended this to me - some high-school English teacher, possibly Deborah Dempsey, must have put it into my hands, and I was certainly an enthusiastic reader of British WWI poetry and memoirs - and I haven't revisited it in adulthood, so I have no idea how it would stand up to adult levels of professional scrutiny, but this may have been the first book I ever read (excluding books by Anthony Burgess!) which showed me that the ways of reading I was already interested in exploring on my own might actually be constituted as something like an actual professional field in the world at large.
3. Orwell's essays. I first read them my senior year of high school, and fell absolutely in love with the voice and the mode of analysis. This has never worn off. I associate bits of Thucydides' History of the Peloponnesian Wars with this period of reading, and both are things I continue to come back to in my reading, teaching and research.
4. Roland Barthes, S/Z. Not at all my favorite work by Barthes (that would be Roland Barthes by Roland Barthes, or some of the essays), but the book I plucked off the shelf at my friend Sara's house the summer after we both graduated from high school (her stepmother had done a master's degree in literature) and read, utterly entranced, when I should have been having a sociable sleepover!
5. Roman Jakobson, "Two Types of Aphasia and Two Types of Linguistic Disturbances" - an essay rather than a book, but it stands here as the perfect instantiation of a kind of structuralism that I absolutely love and that I think I am about to devote myself to reviving in the world. A cluster of other essays also make me think of the intellectual excitement of undergraduate days studying literary criticism: Derrida's "Signature Event Context," bits of Peter Brooks's Reading for the Plot, Genette and Todorov.
6. Simon Schama, Dead Certainties, Unwarranted Speculations. Again, not my favorite book of his, but the one he'd published most recently when I took a life-changing class with him on reading and writing narrative history. In fact, making this list has made me contemplate the extent to which it's my teachers who have influenced me the most (Elaine Scarry, for instance, more by way of herself in person than by way of The Body in Pain - or even Harold Bloom, though I was just one of the masses in that case, not a student with a real working relationship with the prof!) rather than the books per se.
7. Judith Shklar, Ordinary Vices. I actually can't remember when I first read this - possibly not until graduate school - but as an undergraduate I took Shklar's class on political obligation in order to fill the so-called "moral reasoning" core requirement they had in those days at Harvard. It was an excellent class, and I particularly remember her readings of Shakespeare's Richard II and Kleist's Friedrich von Homburgh. The essay on hypocrisy was extremely important for my dissertation/first book.
8. Edmund Burke, Reflections on the Revolution in France. A choice I explained more fully some time ago at Normblog. More generally, the graduate seminar on Burke that I took with David Bromwich in my second year of graduate school had a huge influence on subsequent choices about ways of reading, thinking and teaching.
9. Derek Parfit, Reasons and Persons. A book that showed me how philosophy (the only other major philosophical work I feel this way about is Hume's Treatise of Human Nature) can have not just the intellectual heft but also much of the playfulness and magical qualities of a significant novel.
10. Erving Goffman, The Presentation of Self in Everyday Life. Nothing to say here except that #9 and this one are possibly the two most intellectually charismatic and lively works of recent(ish) years that I can think of; both this one and Reasons and Persons cause me to ache with pain at not having written such a book myself.