This is hard.
1)If I didn't know how to brew, was getting into it, I would go with How to Brew by John Palmer.
2) If I knew how to brew, I would go with Designing Great Beers by Ray Daniels.
I went with John Palmer's book. It gives you a quick overview in the first couple chapters to get you started and proceeds to go into a lot of detail about the entire brewing process throughout the rest of the book.
This question's an easy one for me, as I've only read one book on brewing (The Complete Joy of Home Brewing) - though I thought it was great. I think the idea of RDWHAHB was what convinced me I could make beer.
Randy Mosher's "Radical Brewing" gets great write-ups on Amazon, including some very nice words from Ray Daniels (writer of Designing Great Beers) and John Palmer (the nice fella who gives us www.howtobrew.com).
Radical Brewing is awesome. it's one of the most interesting reads...lots of information, history, recipes...it's not just good for brewing..it's a great book in general.
I have both Papazian books but they're still not up to date enough that I'd recommend them. Go with Palmer's How to Brew if you're really new to brewing and then follow up with Ray Daniels and maybe Jamil Z's brewing classic styles when it comes out in Nov.