The many developers who use the Twitter API have built thousands of creative applications that have certainly exceeded anything that Twitter's founders could have initially imagined when the API was released (for examples of some of these applications, check out our growing list of hundreds of mashups that use the Twitter API).
For over a year developers have been asking for an API from Quora, the Q&A site that has recently exploded in popularity. The company had been waiting until there were "enough users and content on Quora." A browser extension outed the interface and now there is an officially released, but still alpha Quora API.
Checkbox, survey and data collection tool provider, allows developers to integrate survey functionality into third party apps via the Checkbox API. The API enables functionality beyond mere answer collection. For example, developers can integrate a Checkbox survey with a CRM application and automatically create a new entry directly from the survey. The application possibilities are seeming endless.