The Scientist and Engineer's Guide to Digital Signal Processing

Great intro to DSP. If you're looking to build your EE library further, Ron Mancini's Op Amps for Everyone is also available as a free download from Texas Instruments. If you don't already have it, you can get it here: http://focus.ti.com/lit/an/slod006b/slod006b.pdf

Happy to upvote this, even though it's not new. I think this is the best introductory DSP text anyway, and I've got a bunch of them. Its treatment of the various approaches to the fourier transform (and more importantly, why they work) is outstanding.