International
Australian Primary Schools Mathematical Olympiads , Countries with Olympiad Sites, IMO 1995, IMO 1996, IMO 1997, IMO 1999, IMO 2000, IMO 2001, IMO 2002, IMO 2003
National
AMATYC Student Math League, American Invitational Mathematics Examination (AIM, American Mathematics Contest 10, American Mathematics Contest 12, American Mathematics Contest 8, American Regions Math League (ARML), Asian Pacific Mathematics Olympiad, Balkan Mathematical Olympiad, Belgian Mathematical Olympiad, Belgian Mathematical Olympiad (BMO)
Online Contests
ABACUS International Math Challenge, Florida-Stuyvesant Alumni Mathematics Competition, International Mathematical Talent Search, International Mathematics Tournament of Towns, International Olympiad in Mathematical Logic, International Space Visualization Olympiad, Math Olympiad Centre, Mathematical Contest in Modeling (COMAP), MATHmodels, Monthly Internet Mathematics Olympiad 2004
Training
Problem Archives, Greg Martin (UBC), Madras College Mathematics Department Resources, Mathematics Olympiad Lecture Notes, Problem Solving References & Resources, Ravi Vakil (Stanford), Tutorials in Elementary Mathematics for Math Olymp
American Mathematics Competitions
Organization that administers the AMC, the AIME, and the USAMO, with information about the contests, math problem archives, recommended reading lists, and other resources for students interested in mathematics.
Australian Mathematics Trust
Sponsors a number of competitions in the Australian continent.
Crux Mathematicorum with Mathematical Mayhem
Problem-solving journal at the senior secondary and university undergraduate levels.
Math Competition on the Web
Links to national and international competitions as well as training pages for Putnam.
Math Competitions in USA
Sample problems, information and links from multiple contests.
Mathematics Archives
links to contests, problem sets, journals sites.
Putnam Exam Information
Results from the Putnam competition, old exams, and problem archives. Includes problem of the day, selected from over 540 different Putnam, National or International Olympiad problems.
Valentin Vornicu's MathLinks
Math Olympiad Problem Solving site with a weekly contest, resembling IMO in difficulty, with a large math forum and downloadable materials.