The following sites provide various free tools for search engine optimization purposes.
Alexa Rank - A measure of website popularity
Domain Age - Tells you the age of any domain you input
Top 10 Analysis Tool - Tells you where your site ranks among your top competitors for your keyword phrases.
Keyword Density Tool - Returns the frequency of keywords within a domain you enter
Backlinks Tool - Builds a report of all of the backlinks to your domain as well as the anchor text of the actual link
Domain Typo Generator - Provides common misspellings of words so that you can determine if you need to purchase alternate domains.
Google's Keyword Tool - Get new keyword ideas from the best
Google's PageRank - Get links from websites with higher PageRank's
Keyword Position - Returns Google, Yahoo, MSN, alltheweb, and Altavista positions for your keyword phrase
IP & Browser Check - Shows you your IP and browser settings
Search Engine Spider Simulator - Shows you how a search engine spider may view your website
Website Speed Check - Provides the page size and download speed time of your page
Meta Tag Extractor - Enter in a domain and this tool will extract the meta description and keywords tags.
Browser Details - Provides information about your browser and your screen & window settings.