Google Analytics is a free web analytics solution provided by Google, featuring several client-side APIs, as well as REST APIs for Data Export and for Management.
API's that are part of Google Analytics
Tracking Code API
REST API. Can be used to retrieve all management information on Google Analytics: Users, Profiles, Goals, Filters, etc.
Data Export API
REST API. Can be used to retrieve all data that is present on the Google Analytics Interface. It's a read-only API.
Google provide some playground-like tools to let you play and learn the APIs