As soon as Google Analytics was announced, I immediately signed up for it and started playing with it.
The first step was a non-start. Somehow the Check Status function wasn't working for a day and kept telling me that I put the Google code on my pages wrong. But that was fixed pretty quickly.
NOTE: Google email customer service is FANTASTIC. They really respond within 24 hours, mostly sooner! I emailed someone to cancel my Adwords account and it was deleted within 6 hours. I emailed someone regarding the Analytics problem and they responded within 8 hours that someone was working on it. This is in stark contrast to the typical no response or the automated useless response you get from other companies.
Soon data was filtering in. I think Google Analytics is pretty basic. It covers visits and pageviews and I'm getting used to its terminology. It also has nice analyses of the technology used by viewers. I don't have many pages on my site, so I don't know how deep the Analytics goes, but I hope it does go deep.
I am dying to try its ties to Adwords. The conversion tracking should be really interesting. It will also be interesting to see if they are innovative and thoughtful enough on the data display to make it understandable. Often data from websites is so rich that it's unusable unless some machine filters it first, and then presents it in a meaningful way.
Highly recommend this - I just hope Google doesn't ever go "evil" and start using my data for something other than what I would like...
Still the best part of this is that it's FREE.
Try it now at Google Analytics.