Here's the key to finding good math books. Like all general rules, it has exceptions, but if you don't want to wade through masses of math books to find the exceptions, it's good to keep in mind: avoid low-level textbooks.
By "low-level" I mean books written for high school students or typical college freshmen/sophomores who aren't math majors. The quality of textbooks tends to increase as one looks at more and more advanced mathematics. The reason for this is that courses covering higher and higher mathematics gradually grow more focused on self-study and less reliant on the lecturer for providing insights. High school algebra books are absolute abominations; but if you look at a graduate text on, say, group theory, you'll find it's usually great for self-study. However, very few people are at the level of mathematical understanding (or interest!) to read graduate level books. If you're operating at this level, ignore most of what follows. What I'm about to say applies mostly to things like those 10,000 page freshman calculus tomes excavated from ancient Egyptian dig sites.
Textbooks tend to be written with the purpose of being used alongside lectures; consequently, they offer less insight, presuming that to be provided by the instructor, and they have more problems than would be useful to any person self-studying. They also tend to try to present material in the most efficient manner possible, which often means using little prose and structuring the book in a horribly boring and dry format which often consists either of hundreds of examples in a row or theorem-proof pairs.
So what are you left with? In general, with a few exceptions, everything besides textbooks. One of my favorite mathematics books is Visual Complex Analysis. Of all the mathematics books I've read, I've learned the most from this one. Complex analysis is typically left as an advanced undergraduate math course, but this book shows that this isn't necessary; the author brings the subject fully to life with beautiful geometric arguments and clever insights.
Another really fun and interesting book is Dr. Euler's Fabulous Formula. From the title alone, I'm sure you can see that it has more spirit than most mathematics books. It's related to the previous one in that it explores the wonders of the complex numbers.
Presently I've been reading through Geometric Algebra for Computer Science. Geometric algebra, being a Clifford algebra, has very interesting structure, and this book presents one of the most structured introductions I've seen. It's a difficult book--as it must be, for Clifford algebra is not really simple--but it's at a much more friendly level than other books on the subject. This one is aimed at computer science people with a strong math background; other books on geometric algebra are largely aimed at mathematicians or theoretical physicists.