Google Analytics is finally available to everyone, with no waiting for approval. In essence, the program tells you everything you want to know about how your visitors came upon your site and their behavior once they’re there. With the free data provided by Google Analytics, you can direct your resources to marketing initiatives and strategies where they count the most. Without a doubt, Google Analytics is highly recommended.

Google analytics also provides two methods for tracking, a simple tracking cookie and a special system for template driven sites with many pages to track deep into sites. In conjunction with other services you can get alot of information about your site users.
I would also recommend opening a Google webmasters account, as this will give you further feedback about the indexing, pages and usability of your site.
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