I think many readers will be surprised at how accessible "Gödel, Escher, Bach" actually is. I'm not an expert at anything: I have no work experience and maybe two serious computer science courses under my belt, but GEB really satisfies an intellectual curiosity I've had for years. I'm 550 pages in (out of about 750 pages) and with the exception of the two chapters discussing the anatomy of the human brain (a subject I'm just not that interested in), I've torn through this book—I only started reading about three months ago, which means I've been reading GEB much faster than any other book I've ever opened. I highly recommend "Gödel, Escher, Bach" even to those who have seen other people recommend it yet have been reluctant to try it out.
I bought GEB when I was 13, mostly because I liked the Escher paintings. I was hooked after reading the first Achilles/Turtle episode, though, and even though many concepts went over my head at the time. I still haven't read it cover to cover, though, but I still have a hard time not agreeing with this particular recommendation.
+1 Reasons and Persons. The Personal Identity section in that in particular is wonderful! It's a really good book because it kind of stands alone -- you don't need to be very well-versed in philosophy to get the arguments if you read carefully.
I'm currently reading Reasons and Persons. Thought experiments and discussion about how personal identity works under, eg, transporter copies.