I have a few books on my coffee table: How to Photograph Absolutely Everything: Successful Pictures from your Digital Camera Tom Ang Amazon Aimed more at point and shoot, and bridge cameras. Never the less, it's a great starting point with a lot of useful information. Also very easy to read with three of four step break-downs for shooting pretty much any scene. Understanding Exposure, 3rd Edition: How to Shoot Great Photographs with Any Camera Bryan Peterson Amazon More advanced but still easy to understand. Deals with the mechanics of digital photography. Basically everything you need to know to move away from the Auto function. The Photographer's Eye: Composition and Design for Better Digital Photos Michael Freeman Amazon Probably not for the absolute beginner, but included for completeness. Deals with composition and how people look at photos.
I actually found magazines quite useful. Practical Photography run a free course every year (currently running now) and it has proved very useful for a lot of people in understanding the basics.
I got Digital Photography Masterclass: Advanced Photographic and Image-manipulation Techniques for Creating Perfect PicturesFrom Tom Ang as a gift... Not impressed so far really. Good for reading up the basics so far, hope it get's better yet (second half tbd)