Keyword Analyzer: One of the first steps in any SEO effort is to determine what keywords your potential site visitors may be using to find you. Google Adwords offers a free tool for determining this, as does WordTracker. My favorite tool is Keyword Analyzer. It's easy to use, and can run in the background, building a large list of keywords for you, showing you how competive they are, and how many pay per click ads target them. A more popular, but more labor-intensive tool is WordTracker. WordTracker is also more expensive that Keyword Analyzer, because you have to pay a recurring subscription fee rather than make a one-time purchase.
Optilink: Link popularity is the most influential factor in determining web ranking. Usually, sites rank better than yours because their link popularity is stronger. I discuss this here. A free service such as MarketLeap will show you who links to a site, but the best way to find out is to use OptiLink. OptiLink will not only show you who is linking to your competitors' sites. It will show you the Google PageRank of the linking page, how many other links are on the page (fewer is better), and the text in the links (links containing your keywords are much more influential than links consisting of words such as "click here," although it doesn't hurt to have a few of those in the mix, to make your incoming links appear more natural. (As a point of interest, the page for downloading Adobe's Acrobat Reader software ranks #1 for the term "click here," because so many people link to it using that text as the hyperlink.)