Almost a year ago, Google acquired Urchin, a company specialised in providing web site statistics. They renamed Urchin's project to Google Analytics and started a beta for some. Today, it seems Google has opened Analytics for everyone. Get it while it's hot, they really provide in-depth statistics about what's happening on your website.
I tried it out for a few days on my website Holidayhome.be, and experienced all possibilities. Currently, I use Statcounter there, which also provides detailed statistics, but only for the last 100 visits.
One of the nice things on GA is that you can specify up to four goals for your website. A goal can be a user registration, an order, ... GA then tracks how many of your visitors reach one of those goals, and provides you with a conversion percentage. This can be handy to improve your website for better conversion.
Also, there are three different report views: Executive, Marketer and Webmaster, all showing statistics from a different angle. A webmaster might be interested in which browsers are visiting, an executive might benefit to know the conversion percentage.
Anyway, I'm keeping GA on Holidayhome and my blog, it provides in-depth stats and clear reporting.