There are a few free keyword analysis tools available that can prove useful when trying to SEO your site.
The Marketing Brain
Google Keywords Tool
Yahoo Keyword Selector Tool (Formely Overture)
Of these I consider the Microsoft Adlab the best Free Keyword Analysis Tool. It is the easiest to use and shows the number of searches, age and gender distributions and renders all the information in easy to interprate charts and measures.
The google keywords tool is really aimed at Adwords users and has little value for webmasters. It does not show the number of searches for keywords, merely showing the competition amongst advertisers for particular words.
The fact that advertisers compete for search terms will indicate the value of cliks per ad, but is completely irrelivant in terms of analysing the number of searches performed.
The Yahoo Keyword Selector tool is OK when it is working. Often I have found it unusable as it runs so slowly, often timing out. That said, it seems a lot better of late so may prove another useful link. The Yahoo Keyword Selector tool presents a simple list of searches along with the number of searches performed. In a sense the Yahoo Keyword Analysis is a blend of the Microsoft and Google analysis tools, presenting a list of search terms based on a keyword you enter (like Google) but also showing the number of searches performed (like Microsoft).
None of the above tools are adequate for SEO purposes in their own right, however, by using all three it is possible to generate some ideas for yourself.
A good paid keyword analyser is Wordtracker although a free trial is available from wordtracker, it is not really usable, it is meant as a teaser as opposed to adding value to your quest for the perfect keywords. It is also quite expensive to subscribe to, however, it is possible to buy the user of the keyword analyser for a single day, week or month meaning it can be used cost effectively if you can sit down for 24 hours and blitz it!