I would love to have something like this. Checking out Open Badges, it seems cool, but it looks like it's focused on skills, learning, etc. I would like something more generic. Xbox Achievements could be a good thing to look at for something to aim for in that it is defined enough that all games for the system can define them.
My thought is a simple standard api that allows apps to create badges that their users can earn. Users should be able to view their badges not only from the app that created them, but also a way to view all the badges they got from all the apps they received badges from. So the users maybe would have to have an account with the gamification system. Maybe OAuth could be used for apps to get permission to give badges to a user. Apps could also possibly get permission to view a users earned badges from other apps in order to perform some action like give a reward, etc.