trackEvent(category, action, optional_label, optional_value)

Since this can be called in any context, it allows you track something standard as downloads, but for example also whether your fancy drop down menu is actually used.

For details about this, see the documentation on google code or a tutorial. Actually the mentioned tutorial is from 2007 – at this time the functionality wasn’t available to all accounts. It should still be valid though.

To get an impression what can be done with an API, look at Nicolas Lierman’s pictures showing the traffic on his site. I can imagine that based on the new API, more and especially interactive visualisation like this will occur.