Free Search Engine Optimization Tools  

Google Trends: Compare keyword search volume of different terms and see trends over time. One great feature is the ability to analyze audience trends to know if a particular topic's audiences are growing or shrinking. http://google.com/trends 
 

Google Adwords: Advertising keyword research tools for determining search volume, topical relevance and competition. The ability to know the competition for different keywords and groups will help inform whether or not it is feasible to use a particular phrase and rise to the top. Filling a site with a lot of very high volume and high competition terms will normally result in poor search rankings. http://google.com/adwords

Google Webmaster: For existing sites this tool can be used to see how Google already categorizes your site. This is useful in making sure you're not going to lower rankings by making changes. http://google.com/webmaster 
 

Google Analytics:  For existing sites this tool will let you know how users are already finding your content. This also allows you to make sure you don't harm existing high rankings and to identify search trends on your site. http://google.com/analytics

Facebook: Research what users are interested in around your area. Starting a fan page allows you to communicate directly with viewers directly online and see what they are interested in by viewing their profiles. You can also investigate local and regional groups to discover what topical interests are out there that you can provide content for and reach out to them. http://facebook.com/