Try this:
http://piwik.org/

The great thing about it is it gives you all the Google data and it also only requires that you install it on a single domain, and you can track all your domains from that one install. You just need to add a little snip of code to each page you want to track.

However, since you do add the same snippet of code to each page across many domains, you are adding a footprint that all domains are owned by the same person. If you're not doing any cross-linking, this may or may not matter. If it does matter, you can install piwik on each domain.

Not only it is free + self hosted to your server (= the data is yours and google doesn't have to know about it) + it is open source + the results are updated in REAL TIME (unlike google analytics)

There are many modules that extend its functionality (there's even a fake visitors module where the system bumps up the stats on purpose )

You only need to install in on one of your domains and you can monitor multiple websites in that same installation.

Whenever there's an update you get immediately notified and the update is (most of the times) as simple as two button clicks.

I highly recommend piwik!

Now for those who are a bit more on the paranoid side I suggest you check out OWA (Open Web Analytics) http://www.openwebanalytics.com/?paged=5 again open source that records click Heatmaps, Mouse Movements !!! (recording and playback) and Tracking of clicks on all DOM elements.

You can completely replicate your user's sessions to study their behavior and optimize your templates and pages!

Kaan