The Appboy .NET SDK by Marcel Bradea allows communication with the API to implement marketing automation features into mobile applications. Resources include object model, data integrity, and error handling.
Dashlane and Google have (finally!) brought their OpenYOLO password manager to Android. The basic idea is to improve app adoption by smoothing over the login process. Developers can grab the code from GitHub and integrate the You Only Login Once tool with their mobile apps.
Food-sharing mobile photo app Foodspotting had an API since day one. Of course, every mobile app has an API, at least if it needs to store or retrieve non-trivial data. Most of those interfaces stay hidden away, private APIs with only that single, internal audience. Foodspotting, on the other hand, signed Zagat as an early partner and now also has OpenTable, among others, using its Foodspotting API. The company is not exactly making it widely available for any developer, though the documentation is public, planting it in a vast grey area that's becoming increasingly common.