http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...
I credit that book with much if not all my mathematical insight.
Thank you.
(Just seeing that cover leaves me all tear-eyed, reminiscing over that wonderfully irresponsible time.)
replace "that" with "those" ( http://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics ).
the dover books are also a good series, and pretty much anything by Artin is good. i also looked at the Halmos book a couple of people have mentioned.
perhaps one thing to be aware of, though, is that you're not always going to learn things in the linear way they're layed out on the page. moreover, it might be helpful to have more than one book for any given subject. Lang's Algebra, for example, is a really good reference, but a tome if you read it like a text. so you might pick up something small and subject-oriented with a lot of exercises like Artin's Galois Theory or Atiyah's Commutative Algebra, and supplement it with a reference like Dummit and Foote or Lang's texts on Algebra as a whole.
oh, right: whatever book you choose, do the exercises.
The best thing I like about this book is that it often first gives a real-life example of a problem, then gives some history of how the problem was solved, and what the solution was. Even the first chapter was highly illuminating.