If you have the desire to see who visits your website, and how much, Google Analytics is for you.
If you wish to have free professional analysis of search engine terms that point to your website, Google Analytics is for you.
If you wish to see charts, make goals, integrate with adsense, etc., Google Analytics is for you.
Google has made this tremendous project free to everyone. The do have a slight ulterior motive. Google wants individuals to use this tool to help track adsense and optimize their sites for the Google Adsense ads.
But, Google being the mostly awesome company that they are has provided this tool to everyone. Even if you never would think of posting ads on your site, Google will still let you use the tool for free.
Today, I made the decision to create a Google Analytics account and begin tracking stats on my site.
One of the first things I did was to first read a good review on Google Analytics. I then went to Google Analytics Website and signed up for an account. I am so far, very impressed by the interface and the tools.