I've always wanted math competitions on MSE ever since I've joined. These could be either user-held or officially held, whichever seems better. User-held competitions would run as follows.
A user starts a competition with a specified level, with original problems that he/she writes. People sign up or just jump in, whichever. The user posts the problems at a certain time and submissions go in a particular e-Mail address, since there is no Private messaging system on SE yet. Then, the top-scorer wins. Examples of such tournaments can be found on the Art of Problem Solving website. This might be a nice turnaround on SE. Anybody agree?