1] Google Analytics
Web Analytics
Google Analytics is an excellent free web analytics tool. Even if you have another analytics application, we think it's worthwhile to add Google Analytics to your site-- it's that good. We use Google Analytics to report on the performance of the SEOmoz website and our online marketing campaigns. Our only requests? Real-time reporting, a referral report with complete URLs and the option to pay for a service level agreement.
Also Recommended: Yahoo! Web Analytics, Adobe SiteCatalyst, WebTrends
2] Google Webmaster Tools
SEO Insight from Google
Google Webmaster Tools is SEO insight straight from the horse's mouth, and a must-have for any website. Get information on how Googlebot sees your site, view (some) links to your site and edit preferences for how your listing appears in the Google search results. While not as comprehensive as we'd like, it's still a welcome set of capabilities.
Also Recommended: Yahoo Site Explorer, Bing Webmaster Tools
3] Google Website Optimizer
Conversion Rate Optimization
These days, Conversion Rate Optimization seems to be more popular than Harry Potter. Google Website Optimizer is a free way to do simple conversion rate optimization testing on your website. You can test varied landing pages using an A/B test or determine the ideal combination of elements using a multivariate test. Google's tool is free, and capable enough to get you well on your way with CRO.
Also Recommended: Unbounce, Visual Website Optimizer, Adobe Test&Target