Mathematics Competitions Problems and Solutions

Here are links to problems and solutions from various mathematics competitions:

The AMC hosts a William Lowell Putnam Mathematics Competition Directory which contains links to problems and solutions from some previous Putnam Exams.
David Rusin has a Putnam Exams page
Here is the American Mathematics Competitions (AMC) Homepage. Their Problems Source Directory contains information about Mathematical Olympiads and other contests.
Here is the official International Mathematical Olympiad homepage which contains some exam problems.
Here is another International Mathematics Olympiad page.
Here is the Art of Problem Solving (AoPS) page by Richard Rusczyk.

Putnam Exam solutions usually appear on the William Lowell Putnam Mathematics Competition Directory in December, in the Mathematics Magazine in April, and in the American Mathematical Monthly in October or November. Problems and solutions for the 1938 - 1964, 1965 - 1984, 1985 - 2000 Putnam Competitions have been published by the Mathematical Association of America.