Google Analytics
This is the standard tool used to find out how people are coming to your site (direct, search, other sites, etc), what content is the most popular, what buttons/sections are being clicked, and much more.

Google Webmaster Tools
Used mostly by site developers, this tool also allows you to see what search queries individuals have been using to get to your site. It also tells you if you have a slow site, and what might be causing it.

Google Website Optmizer
It allows you to test different versions of a page to see which one is the most effective.

Google Trends
Compare traffic for popular search terms and websites.

Google Insights
Look up keywords and see how much traffic they receive.  You can even look up by country/region, by year, and much more.

Google Keyword Tool
Good place to start your SEO research. Classic tool to find potential keywords.

Google Traffic Estimator
Find out the probable number of visitors a keyword can bring to your site.

Google Ad Planner
The tool you use to screen competitors. Find out how many visitors they get, demographics, what type of interest their audience have, etc.

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