Here's a list that I found today of some free Google tools to help your SEO efforts:

Google Webmaster Tools
URL: http://www.google.com/webmasters/tools/
Benefit: gives you detailed reports about your pages' visibility on Google.

Google Keyword Tool
URL: https://adwords.google.com/select/KeywordToolExternal
Benefit: Find keywords based on other words, phrases or other websites

Google Analytics
URL: http://www.google.com/analytics/
Benefit: analyse your traffic patterns and data to understand your traffic better and to help you see what succeeds and what doesn't

Google Trends
URL: http://www.google.com/trends
URL: http://trends.google.com/websites
Benefit: find out whats hot and upcoming in searches for most popular topics and trends. The first URL shows off trends in search terms, while the second provides traffic trends on sites themselves

Google Insights for Search
URL: http://www.google.com/insights/search/
Benefit: lets you compare and analyze search volume patterns across specific regions, categories, time frames and properties

And of course, don't forget the number 1 tool that google offers, their own search box! Now that instant search is available, you can instantly see what common phrases get searched, and see what sites come up on top of those searches.