Math Forum -- lots of great math information, including weekly
math challenge problems. A good place to begin a search on
numerous mathematical topics or ask for special help with a
challenging problem (ask Dr. Math).
http://mathforum.org
Mathpath -- a summer program for middle school students who are
gifted in mathematics. There is a qualifying quiz which features
challenging problems very different from those in mathcounts.
http://www.mathpath.org