<p>texasdad has done a good job of listing the major math competiions. Further discussion about them can be found at <a href="http://www.artofproblemsolving.com%5B/url%5D">www.artofproblemsolving.com</a></p>
<p>Another list of competitions here:
<a href="http://www.academiccompetition.org/contests.html%5B/url%5D">http://www.academiccompetition.org/contests.html</a></p>
<p>You might also want to consider a math summer program. If you move fast, you can still meet the deadlines for some of them for this summer. A list at:
<a href="http://www.ams.org/employment/mathcamps.html%5B/url%5D">http://www.ams.org/employment/mathcamps.html</a></p>