As far as I know, Google offers at least four sets of API (Application Programming Interface) for anyone to develop their own applications.

Google Web API — With it you can query billions of web pages directly from your own programs.

Google Maps API — With it you can develop location-based services for your users.

Google AdWords API — With it you can write computer programs that interact directly with the Google AdWords server. The API is mainly for advertisers to build application that help managing their AdWord accounts.

Google Desktop API — With it you can develop your own plug-ins for Google Desktop Search.

I am interested to know more about how people use these Google APIs and what applications have been built.