Middle School Students

1. Texas Mathworks Junior Summer Math Camp
2. AwesomeMath Summer Program
3. Mathematics and Related Sciences (MARS) Camp
4. MathPath
5. Duke TIP Program
   
6. Canada/US MathCamp

High School Students

1. Texas Mathworks Honors Summer Math Camp
2. ROSS Mathematics Program
3. Program in Mathematics for Young Scientists (PROMYS)
4. AwesomeMath Summer Program
5. Canada/US MathCamp
6. Mathematics and Related Sciences (MARS) Camp
7. SummerMath (for Girls)
8. MathPath
9. Duke TIP Program 
10. Hampsire College Summer Studies in Mathematics (HSCCiM)
11. Summer Mathematics Research Training High School Camp (SMaRT), Texas A&M
12. MathCEP Summer Enrichment
13. Stanford University Mathematics Camp (SUMaC)
14. Summer Institute for Mathematics at the University of Washington (SIMUW)
15. Math-Science Honors Program (for Arizona students)
16. LEAD Engineering

Other Lists of Summer Camps

• American Mathematical Society's listing of Summer Programs for High School Students
• Art of Problem Solving (AoPS)
  
• Connect a Million Minds Initiative by Time Warner Cable