There are a number of factors coming together to fuel the growth of APIs. Without a doubt, one is the corresponding growth of mobile devices and the distribution of services across multiple platforms. An API is often required to create one native mobile application and becomes incredibly important when supporting many devices. Sometimes these private APIs are made public, sometimes they aren't.
If a mobile application, such as a native iPhone app, provides content or shares data, there's a good chance it connects to a web API for exchanging data. For example, popular photo sharing app Instagram maintains its own contact network and has to let users know when there are new photos to see. Also, whenever a photo is added, Instagram stores it on its servers, tied to the appropriate account. This exchange of data requires the Instagram API, which we reported is meant to be private. But its mere existence was thanks to the app that required it.
Similarly, book recommendation service Alibris recently launched its iPhone app and opened its API the same day. Why? The Alibris API essentially came free with the app because it was required to send search queries and results between its servers and the iPhone.
But don't mistake an API for a developer community. That's the message Instagram sent when it squelched some app using its private API. Though it is technically possible to use the API, the company was wary of setting an interface that it wouldn't be able to change once third party apps count upon it.
Of course, there are often several developer audiences for an API. As Daniel Jacobson explained when he worked for NPR (Jacobson later moved on to Netflix), the public radio company used its API to create a mobile site and apps for Android, iPhone and iPad. The multiple platforms were coded by different teams, but all of them used the NPR API. The outcome for NPR is it doubled its traffic in a year. Mobile users--and the multiple platforms--created a need perfectly addressed by an API.
Whether in support of an official mobile application, or in support of any developer's app, APIs are fueling mobile--and mobile is playing a huge role in the growth of APIs.