What was the book that opened your mind to the beauty of mathematics? Of course, I am generalising here. It may have been a teacher, a theorem, self pursuit, discussions with family / friends / colleagues, etc. that opened your mind to the beauty of mathematics. But this question is specifically about which books inspired you.
For me, Euler, master of us all is right up there. I am interested in which books have inspired other people.

Lots of good answers here. Mine is Hugo Steinhaus' Mathematical Snapshots, which someone gave me when I was a high school freshman. You can order a reprint of the Oxford University Press, New York, 1969 edition directly from Dover for a mere $20: http://store.doverpublications.com/0486409147.html. No need to use Amazon as an intermediary.
I still like my original 1950 hardbound edition better - for (my) old times' sake. I even have a copy of and early (first English?) edition printed in Poland (with red/blue 3d glasses.
Looking back over my published papers I can find the germs for lots of them in ideas I first encountered in Steinhaus - fair division, Appolonian circles, linkages, the normal distribution, coin weighing problems, zonohedra and the stellated dodecahedron (http://www.cs.umb.edu/~eb/stellateddodecahedron/).
