The Google Books API provides access to Google Books, which lets you search for any book and, at a bare minimium, see meta data about it. Depending on copyright status, you might also be able to see sample pages or read the entire book. You can also buy books.
When you find an API to use in your app, you'll need to access it in a specific language - not always an easy or straightforward task. As long as you're doing all that work, why keep it to yourself? Let's look at creating an API wrapper that you can share with others!
Planet OS seems to have found a great number of services that provide scientific/weather/earth related data, regularly download a small sample set from each, and provide a way to access the data through their own API. Let's see what they've got and what we can do with it!
The ISS Notify API (or is it the Open Notify API?) was written by Nathan Bergey for a Science Hack Day competition, then released to the public. You can use it to find the location of the ISS, or to find when it'll pass over a location! Check it out.