In my experience there are no books that could be termed "life changing". Except this one :)
My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.
'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).
The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!
A wonderful book. Buy now!