I liked The Selfish Gene a lot, it definitely stuck with me. But parts of it do get a little tedious. Darwin's Dangerous Idea by Dennett was also good. There are others, like The Blind Watchmaker, but I haven't read it.
More recently I read
Why Darwin Matters by Michael Shermer. IMO, a
GREAT first book to read on the subject.
(I also found
Monkey Girl to be very entertaining, while covering some of the science. And it shows you where the U.S. is legally on the subject, as well.)
In any case, you can get by with out knowing a lot about biology.
I realize you specifically asked for books but I have to add these two resources:
- First, check out this thread that started a here a few months ago:
free DVDsSo far I've watched the one with Ken Miller lecturing...very good.
- Finally, check out some great web resources, like
http://www.talkorigins.org/.