I recently spoke with Richard Zwicky about the Enquisite and the newly emerging field of search analytics. Search analytics is a close cousin to web analytics, but with some key differences. Both use a Javascript tag to collect data about what is taking place on your site, and both use that data to build reports and analyze the data.
Where the difference comes in is that search analytics are focused specifically on the needs of search marketers, and this specialized focus allows it to go much deeper in helping search marketers analyze and optimize their SEO of PPC campaigns. Check out the interview if you want to learn more.