I love little statistics about all sorts of things. I'm sure many visitors of this website (geeks, like me) do.
General stats I'd love a page on this site on which we can see how many people are in each of the levels, how they are distributed, how this is related to their ages or nationalities (genders?) and also how the stars in the practice section are distributed, etcetera.
Problem stats Some funny option to add would be that if I answer a problem wrongly, I would see how many people submitted the same wrong answer. And after I've finished the problem, stats about which different answers came up among the submissions would be cool to know. Also, maybe being able to see how long it took for the users to solve a problem?
Personal stats I'd like to see a graph of when I gained points, which levels I was at on what age, when I got certain stars, etcetera. That would be really cool. It would be like a personal timeline, on which users can add personal achievements, like participation to the IMO (or a medal, even better).