Textbooks
An excellent series of textbooks covering the secondary school mathematics curriculum is produced by Art of Problem Solving. For books that go beyond the standard secondary school curriculum, see below.
Foundations

R. Hammack, Book of Proof (3rd Ed.)

K. Houston, How to Think Like A Mathematician.
Calculus

J. Stewart, Calculus (9th Ed.)

M. Spivak, Calculus (3rd Ed.)
Abstract Algebra

J. Beachy & W. Blair, Abstract Algebra (4th Ed.)
Linear Algebra

H. Anton & C. Rorres, Elementary Linear Algebra (11th Ed.)
Probability

J. Hwang & J. Blitzstein, Introduction to Probability (2nd Ed.)