The Math Forum - wide range of math resources
Planet Math - online encyclopedia
Art of Problem Solving (AoPS) - forums, problems, lectures, information and courses on a wide range of topics and levels.
Wolfram MathWorld - math encyclopedia - for advanced students
Khan Academy - thousands of short instructional videos
Plus Magazine published by Cambridge University
Math StackExchange - Q & A forum for a wide range of mathematics
ArXiv - open access to over 800,000 e-prints in math and math-related fields.
American Mathematics Competitions - AMC 8, AMC 10, AMC 12, AIME, USAJMO, USAMO, and IMO (International Mathematical Olympiad). This set of competitions is for students through 12th grade.
American Regions Mathematics League (ARML)
USA Mathematical Talent Search (USAMTS) – proof based, online, untimed.
Math Prize for Girls - for high-school girls
Harvard MIT Math Tournament (HMMT and HMNT)
Princeton Math Competition (PUMaC)
Math League - runs various state and regional math competitions at elementary, middle, and high school levels.
Bay Area Math Olympiad (BAMO)
Mu Alpha Theta - runs regional, state, and national math contests.
Siemens STS Competition – research competition.
Intel Science Talent Search – research competition.
Purple Comet! Math Meet - online, international, team competition
European Girls Mathematical Olympiad (EGMO) - international competition
China Girls Mathematical Olympiad (CGMO) - international competition
International Tournament of Young Mathematicians - international open problem team competition
Ross Mathematics Program
Hampshire College Summer Studies in Mathematics (HCSSiM)
Research Science Institute (RSI)
Minority Introduction to Engineering and Science (MITES)
Stanford University Mathematics Camp (SUMaC)
Honors Summer Math Camp
MathZoom Summer Camp
Math Path - for middle school students.
Modern Mathematics - International Summer School for Students
The American Mathematical Society's listing of high school summer programs is available here.
PRIMES - year-long mentored research program.
MIT Open Courseware - MIT course materials online.
Udacity - online courses in math and science.
Coursera - online courses.
Math Circles - click here to look for a math circle near you.
Animath - online French mathematics resources and contests.
NRICH - online mathematical resources and forums in the UK.
Estalmat - program for mathematically gifted students in Spain.
Berlin Network of Schools Specializing in Mathematics and Science
Germany Mathematical Society (DMV)
Math en Jeans - team research program in France.