BackLink Analysis Tools
Yahoo Site Explorer - http://siteexplorer.search.yahoo.com
Search Phrase Suggestion and Volume Research Tools
Free:

Google Insights For Search - http://www.google.com/insights/search/
Google Search-based Keyword Tool - http://www.google.com/sktool/
The Free Keyword Tool – http://www.wordstream.com/keywords/

Paid:

WordTracker - http://www.wordtracker.com
Keyword Discovery - http://www.keyworddiscovery.com

Toolbars and Plugins

SEO For FireFox
FireBug
YSlow for FireBug
Privoxy + Tor – This will let you change your IP address for testing.
HTTPFox
LiveHTTPHeaders

Demographics and Analytics

HitWise - http://www.hitwise.com
Compete - http://www.compete.com
Alexa - http://www.alexa.com (Also available as [...]