Any mobile app that does anything interesting has an API. Yet most of the apps that help you get interesting things done do not expose that API to developers. For many of us, a to-do lists are the arteries of our work-life. Some popular task apps that could be integrating the disparate parts of our lives are instead maintaining silos of task data.
Of the apps currently listed as the most popular in the productivity category of Apple's iOS store, only one to-do app has an API it makes available to developers. The Astrid API lets developers tap into the data behind the multi-platform to-do app. The elegantly-designed Clear app recently updated to enable list sharing, but still has no way to access the data. While Clear focuses on its unique user interaction as a selling point, beyond that is that data within the lists that is supporting its users' lives.
ProgrammableWeb lists 38 task APIs and highlighted 5 productive to-do list APIs in 2010. Of that list, all but one have official apps on multiple mobile platforms. The Hiveminder API has been used by developers to create several unofficial apps.
In some ways, a to-do list API without an app makes more sense than a to-do list app without an API. And yet, it's much easier to find examples like Clear or other popular productivity apps that, for some reason, choose to keep their users' data trapped without the walls of their app.