This tool helps you determine whether the site is optimized for a particular local search engine and language.SeoMoz
The tool analyzes the keyword density on the page. Ranks.NL
http://www.iwebtool.com/multirank Let’s say you’re interested in the Google PageRank and Alexa Ranking for a Web page and for 9 of its competitors. This may be done using this tool.
.Fiddler Web Debugging Tool by Fiddlertool.com Tool that analyzes background communication between the browser and the server, ie, debugging tool. It is also free, but for him, the PC must have installed Net Framework 2.0.
http://sitening.com/seo-tools/seo-analyzer/my-analyzer/ Analyzes the page and gives you basic information, so you have insight if something needs to change.
Google Analytics is a superb tool for analyzing sites which Google gave everyone free. This tool gives you information on visiting your site, which links to go visit, what are the countries that are most read pages, unique pageviews, and much much more.http://www.google.com/analytics/
Some of the best free Seo tools! List is not complete, there is still a lot of good tools, for now I have chosen these few.