Hopefully someone will come behind me and correct me, but I do not think that user entered search values are saved to the database.  It would certainly be useful information though.  Sounds like a nice upgrade to be made to  the search provider.

[EDIT]
I just thought of something.  There is nothing to prevent you from creating your very own Search skin object that will indeed save this information for you to query and report on.  I would suggest just taking a copy of the core DNN search skin object, and modifying it with this additional feature. 

Here is a blog entry that I made earlier today to briefly describe the creation of skin objects.  The trick after that is to use the Reports Module to display your most popular queries.
[/EDIT]

eck two wrote I have a step by step instructions on how to add this reporting function to your installation posted here: http://www.innovatasites.com/ecktwo/tabid/3222/Default.aspx

FYI - All of that could be done in an easy to manage and install skin object.