Working with APIs

[d'Anconia]

I was just wondering if anyone knew of a good place to start off learning how to work with API's (Application Programming Interface, for the n00bs). I noticed in a couple of interviews that a lot of employers in the web development industry are working with multiple API's and having abilities in this area would help me land a good job.

What are some relatively popular or common API's that I can start brushing up on to get a better grasp on how API's work? I already know PHP, MySQL, and Javascript (including JSON and AJAX), for reference.

Also, are there any books that you guys would recommend on this subject? I would think that every website / company's API would be different so it may be hard for there to be a generic tutorial or book on the subject.