The free-to-use Pokémon RESTful API (Pokéapi) is linked to an extensive database of Pokémon-related information- a true virtual Pokédex. Pykemon is a wrapper that enables an interface to the Pokéapi from a Python application. The software is supported by the primary maintainer of the Pokéapi, Paul Hallett. It is free-to-use under a BSD license.
There's no doubt that Wikipedia is a giant store of information. And yes, they have an API, but the data isn't exactly structured. But that didn't stop Jim Blackler, who created Quizipedia, a fun game based off of Wikipedia entries.
Battlefield Bad Company is a first person shooter for Playstation 3 and Xbox 360. It keeps an amazing amount of statistics about its players, including a score, levels, a kill count, and many other things. The bfbcs.com site has a good listing of these, in a moderately accessible format. It also offers the Battlefield Bad Company Stats API, so programmers can add this functionality to their applications.