The Art of Problem Solving (AoPS): This web site has a forum for discussion of math problems and math contests, and also administers online math classes for talented students looking for more than their school can offer.

Mathworld: An exceptional math encyclopedia provided by Wolfram Research, makers of Mathematica.

Ask Dr. Math: A great resource to which students can submit questions and receive personal help from college math students. All questions and their solutions are archived, so the site has an extensive collection of interesting problems and their solutions.