There are far too many interesting books out there for me to go back and comment on the old ones, but I might as well make a note of new ones (or old ones that have just come to my attention). I don't claim to have read each book completely, so these are just some first impressions. You can find a few lengthier book reviews here.
Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Mark Ronan. The classification of the finite simple groups is one of the great triumphs of 20th-century mathematics. I envy the mathematicians who discovered the sporadic simple groups, and the last few years of the classification project must have been an incredibly exciting time. For those of us who weren't there, reading this book is the next best thing: it's a vivid account of how the whole story unfolded.
The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele. One of the most beautiful expositions I've seen in years. It's aimed at an undergraduate level but most professionals would learn something new from it as well.
Mathematics by Experiment: Plausible Reasoning in the 21st Century, by Jonathan Borwein and David Bailey. A great book about using computers to explore mathematics experimentally.
Towards a Philosophy of Real Mathematics, by David Corfield. The philosophy of mathematics is a difficult area, since few philosophers know much mathematics and even fewer mathematicians know much philosophy. The easiest thing to do is to stick to mathematical topics that were well understood fifty years ago, or areas like set theory that more philosophers are familiar with. This remarkable book brings in a really diverse collection of modern topics and examples.
A Panoramic View of Riemannian Geometry, by Marcel Berger. This book is huge, and I'm probably never going to find the time to study it in detail, but every time I pick it up I learn interesting examples or motivation. It makes me want to do Riemannian geometry.
Mathematical Logic in the 20th Century, edited by Gerald E. Sacks. A wonderful collection of some of the most important research papers in logic since World War II. For earlier papers check out From Frege to Goedel: A Source Book in Mathematical Logic, 1879-1931, edited by Jean van Heijenoort.
Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition, by Steve Olson. When I was in high school I really wished I could compete at the International Mathematical Olympiad, and I was very disappointed with my contest performance. In hindsight I think many kids take math contests a little too seriously, and books like this one may encourage that, but when I saw it in a book store I knew I had to read it.
Everything and More: A Compact History of Infinity, by David Foster Wallace. This book sounded like a great idea to me, but I found it almost unreadable, partly because the author can't stop making up his own cryptic abbreviations for everything he can think of.