Click that Hood is a game based on open data, built by Code for America’s 2013 Louisville fellowship team.You pick a city, then get a challenge to identify the polygon of a named neighborhood. The "easy" version offers only a limited number of options; the "hard" version has you selecting from all the neighborhoods. I tried Chicago (where I went to school) and didn't do too badly.
The best thing about this game? There's a blank tile for "Add your city" which links to a Google Doc that steps you through literallly, adding your city! I think doing that would be a great project for advanced high school or college GISers!