There are a myriad of free SEO
tools available, and even many sites that list these free tools (the compendium sites are generally supported by advertising, and must therefore practice good SEO themselves to be successful!).
Some good sites that list (and provide links) to free SEO analysis tools http://www.trugroovez.com/free-seo-tools.htm, http://www.webuildpages.com/tools/, and http://www.seocompany.ca/tool/11-link-popularity-tools.html.
Some of the most useful (and free!) single-purpose SEO tools are:
NickeBot: a keyword discovery tool that helps pinpoint the right keywords for optimization, http://www.nichebot.com/.
The SERPS Tool: the SERPS (or Search Engine Positioning) tool helps you discover your ranking across Google and other major search engine in one fell swoop, http://www.seo-guy.com/seo-tools/se-pos.php.
Meta Tag Analyzer: checks meta information for errors and relevance to page content, http://www.seo-guy.com/seo-tools/se-pos.php.
These tools can definitely be time savers, particularly if you have a large amount of content you need to optimize. The price is certainly right!
Individual tools also can serve as a reality check: by running your pages through one of these tools you can get a pretty good feeling for how well you have optimized a page. However, you should bear in mind that there is nothing that one of these tools can do for you that cannot also be done by hand given the knowledge you have learned from this article.
Individually, SEO analysis tools available on the Web can help you with your SEO tasks. However, to get the most from these tools you need to understand underlying SEO concepts, as explained in this article, before you use these tools.
Over time, as you progress with SEO, you will probably accumulate your own favorite SEO analysis toolkit.