Google Analytics is a free tool from Google that can let you examine users' behaviour on any site.
It can be hooked up to Google Adwords, but it can also be free-standing.
Once you have signed up, Google will give you a small piece of code to place in the HTML of your website, which sends information back to Google. Using this information, Google can give you graphs and usage statistics, including a breakdown of referring websites and search engines.
You can also use Google Analytics to track goals - for example, downloads and forms being filled in. Attaching separate pieces of code to these events means Google can let you see how users are being funneled into these events.
To give it a try, browse to: http://www.google.com/analytics