Hi

In last six month I have tried to optimize my site for the Search engines. When doing so I am constantly looking at some of the sites/tools to know the position of my site in regards. These are publicly available free tools and shows statistics for websites. Here is a list of things that people might be interested, in context of there site.

Technical data of a site

IP Address - by DomainTools Search

Other Sites on an IP Address - by IP Query at Live.com

Name Server - by DomainTools Search

W3C Validation for the site page - by W3C Markup Validator

CSS Validation - by W3C CSS Validator

Statistics on the popularity of the Site

Alexa Rank - by Alexa

Alexa Reach - by Alexa

Alexa Page Views Estimate - by Alexa

Google Trends Data - by Google Trends (only available for High traffic site)

Ranking.com Rank - by Ranking.com

Netcraft Ranking - by Netcraft

Bloglines Subscribers - by Bloglines Feed Search

Data on Search Engine Indexing

Google's Indexed Pages - by Google site: command

Yahoo! Pages Indexed - by Yahoo! Site Explorer

MSN Pages Indexed - by Live.com  site: command

Ask.com Pages Indexed - by Ask

Gigablast Pages Indexed - by Gigablast Advanced Search

Data about the site linking.

Yahoo! Link Data - by Yahoo! Site Explorer

echnorati Link Data - by Technorati

MSN Link Data - by Live.com link command

Google Link Data - by Google link command (This data is always inaccurate)

Google PageRank - by RankAlert

If you have any more links to add to this feel free to share. 

Hope this helps
Thanks
Vikram