An API is a database kept by an entity which allows developers (programmers) to access its data through a particular protocol. Programmers can get a key that allows them entry into the API; they can then gather the data and display it.
Here are 3 APIs that I found:
1. The NASA API at https://api.nasa.gov/
The NASA API gives access to items such as the Astronomy Picture of the Day, Mars, and Earth pictures. There’s an API access endpoint, documentation, and a getting started guide. There’s an hourly limit of 1000 requests per hour. An API key is recommended but not required (no authentication needed). GitHub has 169 results on a NASA API search.
2. The Goodreads API at: http://www.goodreads.com/api
This API grants access to a lot of information about authors, book reviews, etc. There seems to be less information about single titles, but one can get lists of books as well as entire virtual bookshelf. One can acquire a developer key and there are instructions as to how to how to use the API. The site also has links to a developer’s forum. GitHub shows 95 results for the Goodreads API.
3. The United States Census Bureau API: http://www.census.gov/data/developers/data-sets.html
This site lists about a dozen categories of survey data. In each category, there’s a summary file and data file with sample calls. Users can get an API key. There’s an API forum and technical documentation. GitHub shows 125 results for the census API.
For more APIs, there’s a directory at: http://www.programmableweb.com/apis/directory