Keywords with the most search volume are generally not the best keywords for which to optimize your site. The ones with the most search volume are usually the 'general' terms that don't convert...
For example, if you have a loan site on the internet, you are wasting your time trying to optimize for 'mortgage'. 1) it's a HIGHLY competitive term. 2) it's very general and has a VERY low conversion rate. You're better off optimizing for things like "Low interest home loans" or "mortgage refinance loans".
The term "TV" will get far more searches than "Samsung flat screen model 282881", but people searching for "Samsung flat screen model 282881" will convert at a MUCH higher rate, people searching on "TV" will almost never convert - they're shoppers just beginning to research a purchase typically" or maybe they are not even looking for a TV... perhaps they are looking for a TV show.
Regardless, KeywordDiscovery and Wordtracker are the two most well know freebies... Overture flat out sucks and is almost never up and running these days.
IMO your best free info will come from 1) your web logs and conversion data (if you track it), 2) your PPC campaign conversion data and 3) looking at your competitors websites - poking around paying specific attention to their title tags to see the keywords for which they are optimizing content on specific pages. You can learn a LOT by looking at your competitors...
Using the keyword tools to suggest potential keywords that you might not have thought of is a good idea. Just remember 1) just because it is searched on a lot does NOT necessarily mean it's worth the effort to try to create pages/content to rank for that word because it may not convert and 2) the numbers these tools put out are skewed by things such ranking tools hitting the search engines to see how a particular site ranks for a particular set of keywords in each industry.
So the # of searches listed by these tools on a rarely searched term is probably much more accurate than the # of searches listed for a popular term because no one's ranking tools wil be checking the rare term so the number will be fairly accurate, everyone's ranking tools will be checking the popular term so the number will be grossly overestimated.
My opinion... Everyone has one. :)
PS: I agree that using PPC to test out whether particular keywords will convert before building actual pages that rank for those keywords is a quick way to gauge how much traffic you might get if you showed up on page 1 of the SERPs on organic search as well as how well those terms convert once people click on the paid link. If you see the PPC campaign for those terms are converting, it would lead one to believe a page that ranked on page 1 in the SERPs would convert at a similar rate.
[edited by: ZydoSEO at 8:00 am (utc) on Dec. 16, 2007]