The NSF also has a list of REU's in other scientific fields. You can select a field here.
Also bear in mind that your professors tend to know a thing or two about research, asking them for suggestions is okay.
A well-written set of notes covering calculus, the basics of differential equations, and high school algebra. About the same quality as any of the textbooks on this subject, and they're free.
Has a huge list of difficult problems.
Has a surprisingly large collection of proofs. Much easier to look here than hunt through the library for a specific proof.
Online community for answering basic math questions. If your question pertains to undergraduate mathematics, you should ask it here.
Similar to math stack exchange, but for advanced mathematics, e.g. research level mathematics.
Books that Are Actually Useful
A reasonably accessible introduction to general topology. Covers all of the basics. Has quite a lot of content, and it's quite cheap.
Relatively easy to read.
A genuinely enjoyable read. Covers the theoretical aspects of linear algebra.
One of my favorite books. Measure theory is very interesting, and Halmos is an excellent writer.
Try chapters three and four for a good minicourse in analysis. The rest of the book focuses on vector space calculus and manifolds.
Rudin is pretty well known as a writer. The book's good. I suggest reading a book on measure theory first, because he moves very quickly at the start. You can find cheaper versions than the one here. Bear in mind that this book covers exclusively graduate analysis. If you want an introduction to analysis, look elsewhere.
Books for Fun
A Course in Arithmetic - Jean-Pierre Serre
An easy introduction to arithmetic. Worth reading even if you already know arithmetic.
Basic Number Theory - Andre Weil
Another easy introduction to one of the core fields of modern mathematics.
Basic Algebra I and Basic Algebra II - Nathan Jacobson
The last of the three "Textbooks with Incredibly Misleading Names." Still pretty good, as mathematics books go.