When you talk about analyzing search data you spend your time focusing on what words you are ranking for and how many people these search engines sent to your site. What is often over looked is internal search data. That is what words users typed into your internal search tool and the results it gave them. This data is not often captured by your standard website reporting tools.
Google analytics has recently added this ability but depending on how your search is created, it may not work for your site. It also will take more work to setup then normal analytics. But the goldmine of data you can find there will be well worth the extra time. This data is especially interesting for sites with shopping carts but can reveal interesting information about your users on normal sites. It could also shed light on navigation problems. If one item is searched for overwhelmingly compared to others, it may be a sign that you have to alter your navigation to make that item easily accessible.
Entry by: mick