I haven't heard many stories about cool things built with the Google Analytics API. Care to share your stories?
Check out the Google Analytics Application Gallery, Google's official showcase of things built to augment Google Analytics, both via the API and by way of modifiying the tracking code.
As far as personal preferences, PadiTrack is pretty great, as are most of the current Editor's Picks.
I have created embeddedanalyitcs.com. Our concept is built around leveraging data from the Google Analytics API for web publishers who don't necessarily have the skills to utilize the API. Currently we have two primary services:
EmbeddedCharts This is a service which allows you to create charts using any combination of dimensions, metrics and time frame (e.g. last 7 days, 30 days, year). You can then embed these charts into your site simply by copying code contained in an iframe tag. Long ago (before the API was released) I wanted a way to cull data from my Google Analytics to show daily visits for potential advertisers. At the time I was using the scheduled email export and parsing the email. This was a pain. Then came the API and this made it easier.
Inbound LinkAlerts This is a nifty little service which alerts you of newly detected links pointing to your site. Essentially we query your GA account for all existing links to your site. Once this "data warehouse" is created the service periodically (hourly or daily) queries inbound links for the last day. These links are compared against the data warehouse and if a new one is found it sends you an email alert.