Valladolid Problem Set Archive - This site contains an archive of many many problems that have appeared in programming contests held by ACM. You can sign up, get an account and use their online judging system to test whether you solved the problem or not. The site also contains a useful message board for help on solving problems. AKA: "The UVA Judge"

ACM ICPC - Here you can find out information about the ACM contest, past regionals, and past problem sets.

APICS Archive - This is an archive, hosted by DAL University, of old APICS competition problem sets, results, and judge's test cases. It's a good place to get an idea of what kind of problems we are expected to solve.

ACM ICPC Problem Archive - This is a very useful resource, it contains past problem sets from regionals all over the world. Many of them have judge's test cases and sometimes solutions.

Number Theory - This site contains a dump of many number theory ideas with explanations. Knowing your number theory is very useful for these types of competitions, there's often a question related to this area of math.

Steven Halim Website - Contains a list of problems Steven has solved with hints about how to solve them. He rates the problems with difficulty ratings, and he also has them categorized based on the type of problem they are.

Valladolid Problem Hints - This site is similar to Steven's. It contains a list of problems and hints about how to solve them.

ACM Beginner - A very good site with a list of problems the author has solved along with his analysis. He also has tutorials on topics such as big integers and number base conversion.