The data Google give back to you in Analytics may be "anonymized and aggregated", but the data you're allowing them to collect from your users on your behalf is certainly individually-identifying and specific (and shareable with the NSA either wholesale via some PRISM-like means, or at the very least via court order or NSL)

I've been told Piwik (http://piwik.org) is very good. I'll give them a shot. If they're good enough, maybe I'll replace Google Analytics with them - then at least I own all the data myself.