An approachable book on algorithms

This is not very approachable.

I highly, highly recommend Skiena: http://www.algorist.com/

Skiena has much, much more content on the motivation behind algorithms and algorithm selection than other algorithm books. It also dives headfirst into graph traversal, which "Algorithms-in-C"-type books tend to leave for the end of the book.

Other decent algorithms books are CLR (http://j.mp/91SqgE), which looks pretty on my shelf but I never use, and Knuth, which I find works better as literature than as a reference, but highly recommend anyways. Avoid Sedgewick.