I was wondering how long it would take for a book thread to appear, and I'm pretty impressed at the posts.
There are 2 "books" that I rank as the most influential to me...one is the Federalist Papers. The outright brilliance and forethought of this government's Founders is astounding. It also makes me wistful for an era in which the limited means of communication ensured that ideas were well communicated, mulled over, and thoughtfully debated. I often think about how profound men like Jefferson and Hamilton would be in today's world, where they could discuss their visions through Twitter and blogs and such...and my guess is that they'd be much less cogent. By essentially hand-writing letters back and forth to each other, they really had to think about what they were saying.
The other is Administrative Behavior, by Herbert Simon. As one who studied government, it's the opposite end of the spectrum from the Federalist Papers; rather than outlining broad ideals that government should be built upon, it digs into the actual structure of government to find out how it works, and how it should work. Simon is an absolute genius, but I don't recommend it to anyone who's not interested in how organizations function.
As far as favorite books go, Orwell's 1984 and Dashiel Hammett's The Maltese Falcon are two books that I cannot put down once I start reading them. It's amazing how the way words are arranged on a page can be so suspenseful and captivating.