The internet is wide, so there are too many places to look for some good staff when you need it. While loving math and programming, I discovered the world of programming competitions, contests, problem sets, and other tasty things. So not to lose them I will post them here.

Problem sets with instant checking

• projecteuler.net A lot of problems, any language, increasing complexity (if you'll be able to use brute force for solving first problems, after some time, brute force will only stuck your PC for hours), new problem each week. At now more than 300 problems.
• codechef.com A lot of problems, 5 difficulty levels, 35 possible languages, new problems.
• codeforces.com You can read more about this in second list, but the main idea that you can practice on problems from contests that ended and in which you didn't participated.
• codegolf.com Nice idea to write less code. Only few problems, but you'll spend hours if no days to make your code less and less. Available Perl, PHP, Python and Ruby.
• spoj.pl ~2k problems to submit, also are some problems for which you can discuss with judges, many languages.
• acm.timus.ru >800 problems, Pascal, JAVA, C, C++, C#.
• uva.onlinejudge.org ~2k problem, divided in categories, but quite slow web site. C, C++, Java or Pascal.
• codingbat.com Online codding practice for Java and Python, starting with very low level
• www.spoj.pl A huge amount of problems, more than 30 languages
• golf.shinh.org Problems of short codding, many new problems, many available languages
• acm.mipt.ru Many test problems, with instant checking, aroung 8 languages to choose

Programming competitions

• code.google.com/codejam Google code competition. As prizes there are money, and other stuff.
• codechef.com Many competitions, this site supports other initiatives by hosting or organizing problems submissions.
• codeforces.com Also a lot of sub competitions for small intervals of time(~2h), for some of sub competition are given a certain language for solving. In each sub competitions you get points also in dependence of time, and you can submit hacks(problems test) for different users, and can gain or loose points.
• topcoder.com Very big community, a lot of categories, also design and other stuff. There are also competitions for big teams, that compete in creating something big.
• codefest.org.in Code Fest, in 2011 is second edition, 28 Jan to 20 Mar, 5 categories(different competitions), C, C++, Java and Python, money prises.
• spoj.pl There are very often competitions.
• uva.onlinejudge.org Quite often are organised competitions.
• acm.mipt.ru Publishing from time to time different russian programming competitions

Other types of fun codding

• pythonchallenge.com Each page has a hidden challenge, and to go from one page to another, you have to solve some puzzles (easy solvable if using some programming language like python), many hints for Pyhton
• rubyquiz.com Quizes for Ruby, site is no longer active, but there is activity on mailing list
• gowrikumar.com/c quizes/puzzles in C
• www.facebook.com/careers/puzzles.php Puzzles from facebook
• programthis.net/challenges Few challenges, help in comments, looking for creative solutions
• ocf.berkeley.edu/~wwu/riddles Problems collected from many places, many of them from job interviews
• programmingpraxis.com List of problems to maintain your skill and brain
• smartscholar.com/computer-science-guide Computer science resources for students