"Gödel, Escher, Bach" by Douglas Hofstadter, which I read when I was 17. I was just getting into serious programming (I would learn C later that year). I had only an inkling about things like recursion, had little appreciation for music outside of Pink Floyd, and lacked any kind of spiritual philosophy that didn't end in simple atheism or nonsense that I stole from science fiction paperbacks.
GEB got me wondering about a lot of things, and showed me how hard science and engineering and art can coexist. It's not a perfect book -- frankly, I find it rather dull reading now -- but it was an eye-opener when I was just starting out.