You can download Piwik and install it on your own server to gather analytics data that could replace your usage of Google Analytics. In my personal opinion, it is always nice to have two services running to make sure you’re getting the right analytics data or still have data in case something happens and one service breaks.
What seems pretty neat about Piwik is the fact that it works with plug-ins so you can add and remove functionalities that are suitable for you. The service runs on php and MySQL so it should be an easy install process, the site says less than 5 minutes.
They’re on version 0.2 right now but give it a try, their online demo sems pretty awesome.