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).
Pearson, a household name in the education and training markets, typically brings traditional study materials to mind (e.g. thick study books, video lectures, etc.). However, Pearson recently launched its fifth API showing a dedication to innovation and meeting the rapidly changing technology scene where Pearson students live on a daily basis. Pearson's latest API, Nursing and Health Survival Guides API, allows developers to integrate data from Pearson's highly acclaimed Nursing guides into an application of choice.