If you are utilizing Google Analytics it is a simple matter to track your on-site search feature and gain insights into what users are typing into your search box.
These instructions are for MightyMerchant (http://www.mightymerchant.com) customers, but armed with these instructions, you should be able to pretty easily figure out the configuration for other systems.
1. Log into Google Analytics.
2. Under the “Actions” column, click the Edit link.
3. Edit the Main Website Profile Information.
4. Turn on the Site Search feature and enter your settings.
At the simplest level, you just need to turn on the “Do Track Site Search” setting and specify “keywords” as the Query Parameter. (note: systems other than MightyMerchant could use a different query parameter.)
5. Once you save your changes, Google will start tracking your site search activity within 24 hours.