There were a couple of old questions on Meta that had a lot of good ideas.

[What do you want to build with the SO API?][1]  
[What would you want to see in a StackOverflow API?][2]


  [1]: http://meta.stackoverflow.com/questions/35723/what-do-you-want-to-build-with-the-so-api
  [2]: http://meta.stackoverflow.com/questions/12224/what-would-you-want-to-see-in-a-stackoverflow-api