What SEO tools do you regularly use?

I primarily use Google Analytics.
Apart from that some of the tools that I use are;
Keyword Analysis Tools / Keyword Research Tools    (DP keyword suggestion tool & Google Keyword Suggestion Tool are popular)
=> Keyword Density Tools
=> Index Checking
=> Backlink Checking
=> HTML validation Tools    (W3C HTML Validation Service – validator.w3.org/ )
=> Google Pagerank CHecker    (Google Toolbar)
=> Google Webmasters Tool (along with Yahoo Webmasters Tool)
=> XML Sitemap Generator
=> Search Engine Submitters (IBP is good)
If you have a limited budget, Google webmaster tools, Google Analytics and SEO for Firefox should be sufficient. If you are using a CMS like WordPress, they come with a whole lot of SEO Plugins that are completely Free.