If math is about measurement, then Mathletics may have your child's number. Much like games that post the best scores of players, the Mathletics SOAP API makes student scores accessible to programs as well as its website.
Twitter has reversed its decision to shut off API access to Politwoops, a service that tracks and posts the deleted tweets of politicians. Twitter shut down API access for the U.S. Politwoops site in June of last year, and the remaining Politwoops websites lost API access a few months later.
Flexpaper is an open source document viewer--and it is beautiful. The Flexpaper API lets you incorporate your publications into other applications. Flexpaper works on virtually any device and is, no surprise here, flexible. It can display in HTML, HTML5, Adobe Flash or any combination of these.