Note: As of November 2005, this is pretty out of date. Most of these books were listed a few years ago in my first couple years of undergraduate. Since then I've read other books and my interests may have shifted somewhat.

Some books I've read or am reading and particularly like:

	Gödel, Escher, Bach Without hesitation, the best book I've read. Extremely thought provoking.
	The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems Martin Gardner, famous purveyor of recreational mathematics, used to write a column in the Scientific American called "Mathematical Games". This book is a (very large) collection of some the best installments. Each chapter is a bite-sized chunk of fascinating mathematics, suitable for one to four hours of reading and thought.
	Metamagical Themas After Martin Gardner stopped writing his column in the Scientific American, Douglas Hofstadter began writing a replacement entitled "Metamagical Themas" (an anagram of "mathematical games"). This book is a collection of those columns. The ones about social dilemmas are particularly interesting.
	Surreal Numbers In this unusual book by Knuth, set theory is presented in the form of dialogues between two fictional characters. This book is a very enjoyable read.
	Engines of Logic This book chronicles the development of mathematical logic, especially as it relates to computers. The characters include Boole, Cantor, Gödel, Turing, and more. This is the area of mathematics I find most interesting. See also this blog entry.
	Zen and the Art of Motorcycle Maintenance An interesting sort of philosophy book. Highly recommended.
	Candide Humorous and ironic.
	Fantasia Mathematica A collection of short stories from various sources that all have something to do with mathematics. A fun diversion.
	The Hitchhiker's Guide to the Galaxy (and the others in the series) The funniest books I've read. Very clever. The humor is reminiscent of Monty Python and the Monkey Island adventure games.
	1984 A classic. Absolutely essential reading for anyone living in modern times.
	Down and Out in the Magic Kingdom Available free on the web (pdf and ascii text), this was a relatively short, enjoyable read. I think its ideas about the future with respect to the importance of reputation are insightful. By web personality Cory Doctorow.
	The Oxford Companion to the Mind This is an encyclopedia of topics related to the brain and thought. It's fun to flip open to a random entry and read it.
	Artificial Intelligence and Natural Man Thoughts on AI from the perspective of a psychologist.
	Pattern Recognition Somewhat outdated, but it has these great visual pattern recognition problems in the back that do a lot to get you thinking about things.
	The Character of Physical Law A collection of very readable physics lectures by Feynman.
	The Art of UNIX Programming A big hodge-podge of practical wisdom from the UNIX world on many aspects of software. When Eric Raymond isn't wallowing in aggrandized descriptions of "hacker culture", he has good things to say.
	Forever Undecided This book presents a cute treatment of some of the ideas of mathematical logic and formal systems in the form of knight and knave (i.e., truth-teller and liar) puzzles and reasoners who consider their own beliefs. If you already have a familiarity with basic sentential logic and have seen a puzzle that starts something like "You are on an island where there are two groups of natives; members of one group always tell the truth and members of the other always lie ...", then you will probably want to skim over the first few chapters. Once the book introduces the concept of reasoners considering their own beliefs (the analog of sentences in formal systems that assert the provability of other sentences), however, things start to get really interesting.
	A Mathematical Introduction to Logic If you want to learn about mathematical logic, I recommend this book. I found the book uniquely agreeable. Most math books have at least one or two annoying quirks (e.g., important material given in the middle of examples, unequally distributed rigor, needless attention to messy details that could be eliminated through better definitions), but this one was pleasantly free of such problems. Reading it was always a joy for me.
	Introduction to the Theory of Computation I had to read this for a class, but I really liked it so I'm including it anyway. Provides a concise introduction to theoretical computer science.
	The Design and Analysis of Algorithms I also read this one for a class. Unlike other books on algorithms, it focuses more on classifying algorithm design techniques rather than just enumerating important algorithms.
	The Code Book A fascinating history of cryptology from the Caesar shift cipher to RSA.
	Applied Cryptography Contains information about a plethora of cryptographic protocols along with practical advice about implementing modern ciphers. You really ought to read its section on the protocols; what can be done may surprise you.
	Lecture Notes on Cryptography This isn't actually a book, but rather a very book-like set of lecture notes (it appears that the authors intend to publish it as a book at some point) by noted cryptographers Goldwasser and Bellare that is available online. Applied Cryptography (above) is nice for people interested in using cryptographic techniques, but this is a great place to look if you are interested in cryptography from a research perspective. It is a good introduction to how modern cryptography is placed on a rigorous mathematical foundation of complexity theory. I've only read parts of it. The parts I've read have been right at the edge of my mathematical abilities (as a senior undergraduate) and maybe even a bit intimidating at first, but well worth the effort.
	Designing Embedded Hardware Embedded systems are fun because you get to deal with many levels of abstraction at once. General purpose computers are so complicated that you can only think about one aspect of them at a time.
	TCP/IP Network Administration This book hit the spot for me, doing a good job of filling in many gaps in my knowledge of networking and the Internet. You don't have to be a network administrator to enjoy a better understanding of how the networked world works.