There have several free SEO tools like Google adward, Google Wonder-Wheel, Google webmaster and analytics. Google wonder wheel is a really good tool to find out low competitive Keywords.
I'm glad that Google Wonder Wheel is back as Contextual Targeting though not as intuitive as the original Wonder Wheel but still glad to see it back. Agree Google Webmaster tool and Analytics are good tools but a little wary of Analytics as many SEOrs have warned me of using it as they believe that Google uses it to spy on your site.
SEOmoz tools you can better handle everyday SEO tasks. You can analyze keywords, research back links, do on-page analysis, find accessibility issues and track rankings all in one easy-to-use management platform.