Open Site Explore is a great tool that allows you to gather information on backlinks to your or your competitors websites. It is totally free and very useful!
The AdWords Keyword Tool is a great tool to check things like approximate monthly search traffic of specific keywords, competitor keywords, synonyms that can be used as keywords, competition over keywords etc. It is free and easy to use.
Google Trends for Search is a great free tool to compare searches between up to 5 keywords. You can be very specific geographically as well, plus see historical trends of searches on those keywords.
Stay tuned for more SEO tools……