Most mashups rely on some type of API that's freely provided by a public web site. ProgrammableWeb tracks thousands of these resources across dozens of categories. Generally, these interfaces are SOAP or REST-based, but they may also work in cooperation with other open formats like RSS or Atom. In an enterprise setting, mashups have a more diverse set of protocols to potentially leverage including JDBC/ADO.NET (databases), SMTP/IMAP (email), and SNMP (network monitoring). Unless you are building a data mashup, one of the participants API's is usually focused on visually representing the data. It could be the classic Google Maps API, or perhaps some type of charting (Google Charts is a great resource).
The Open Library is a project of the non-profit Internet Archive, whose long-term goal is to present "one web page for every book ever published." A recent release of the Open Library brought the total number of book records to over 13.4 million (including over 234,000 records with full-text for the book).
I'vRead is a service for keeping track of what books you've read. Seems simple, but it can be rather useful for those of us obsessed with reading like myself. Its web site offers the service for free, and using it is already pretty simple. There isn't even another account to register for. All a user needs to do is add a specific tag, @ivread, to a Twitter post mentioning the book. It allows for some basic searches of the data on their website, but the I'vRead API is where the service really shines.