Tony Woodlief, Megan McArdle, Ilya Somin and others tackle the question, "what three books would you recommend to someone who disagrees with you?" Although Tony frames it as a left versus conservative/libertarian discussion, given the sort of "I don't agree with either party" mindset most small-L libertarians share, I think this would be more dependent on where that disagreement is than it would be a standard three books that could possibly wrap up the strongest arguments for an/my individual way of thinking. I mean, a free market conservative with social conservative biases would get much different treatment than a traditional ACLU-type liberal lacking a decent respect for property rights and economics. Indeed, I could probably come up with a list for a lot of traditional libertarian types, especially the consequentialist economist types.
It is assumed that these books would be more friendly to the intelligent layperson than some of the books that cater to the wonkish types that are typically answering this question on their personal blogs.
Staying within Tony's framework, however, I would give:
Economics in One Lesson by Henry Hazlitt
Government Failure: A Primer in Public Choice by Gordon Tullock et al.
The Cult of the Presidency by Gene Healy
I picked Gene's book not because of any personal or collegial affinity I have for him, but because I think it is an excellent, non-partisan attack on the absurd heights we have taken the expectations of the most visible political office in America. I picked Hazlitt's book because it is a concise explanation of fundamental economic concepts--and fallacies--that have been prevalent in modern Western economic discourse. And Tullock's book, I think, is a nice bridge between the other two because it explains the confluence of the political and the economic arenas that make sense on an almost intuitive level. They are all eminently readable--I dare say "enjoyable" in regards to Gene's book.
I will soon post books for the Right and the "Libertariat" in the next day or two.