20,000 Problems Under the Sea
Database currently contains 20,945 math problems from 38 journals and 21 contests.
Arkadii Slinko's Math Olympiad
Collection of contest problems from New Zealand Math Olympiads and Auckland Mathematics Olympiad.
IMO Problems
International Math Olympiad problems and solutions from 1959 to present, collected by John Scholes.
International Mathematical Talent Search
Solutions and Comments.
Internet Mathematics Contest Problems
Contest questions from the 1998 Douglas Zare's internet contest.
Kalva
Complete set of all International Mathematical Olympiad problems with solutions. Also includes problems sets from other national and international contests.
Kiran Kedlaya's Math Problem Directory
Sources of information about mathematical problem-solving. Focusing on long-answer type problems found on Olympiad-type contests or in problem sections of math journals.
Madras College Mathematics Department Resources
Problems from UK Math Olympiads and a collection of training materials.
Math Olympiad Problems from Around the World
In particular, from Iran.
Math Olympiads
Collection of problem sets from International and National Mathematics Olympiads.
Mathematics Problem Solving
Old sample problems from Putnam training sessions, by Monica Nevens (University of Ottawa).
Olympiad Math Madness
Jeffrey Lockshin's collection of mathematical problems, invented for mathematical olympiads all over the world.
Problem Page
Archive of problem sets and solutions from Wisconsin Mathematics, Engineering and Science Talent Search.
Problem Writing For Mathematics Competitions
Mathematics problems for middle school and high school math competitions with topics range from algebra and geometry to probability and trigonometry.
Prof. W. Kahan's Notes and Problems
Large archive of problems and solutions from Professor Kahan's Putnam Problems Practice Seminar.
Putnam Problem Solving
Supplementary problems and related links by Byungchul Cha (Johns Hopkins University).
Resources for the Putnam Mathematical Competition
Three sets of practice problems in PDF format compiled Yang Wang of Georgia Institute of Technology.
Singapore International Mathematics Olympiad
Training resources include problems and partial solutions.
The Putnam Mathematical Competition
Practice problems for Putnam competition in postscript and PDF format. Page organized by Harry Tamvakis (Brandeis).
Tournament of Towns at Toronto
Contest problems and solutions for The International Mathematics Tournament of the Towns.
Union College Putnam Club
Problem sets from weekly practice sessions.
USA, International and Asian Pacific Math Competit
Problems for the US Mathematical Olympiad (1989-2003), International Mathematical Olympiad (1986-2003), Asian Pacific Mathematical Olympiad, and the Team Selection Test.
USSR Math Olympiad, 1961-1986
Problems without solutions.