The intranet I look after was asked to provide the kind of metrics you're speaking about.
As the other posters have pointed out it is very hard to do appropriately, and very easy to do inappropriately e.g. HIT count
We've ended up giving the big dogs what they want Search lead to page, by tagging all the links presented in the search results with a URL parameter, that we can then quantify using the HTTP logs
We present the number of pages that were viewed as a result of a search.
Keeps the high ups happy - doesn't mean much really.
Failure
The very very useful thing that has come out of this is that we now check the search logs for situations where there have been ZERO results returned.
For each of these users we send them a link to the information they were looking for, if we can figure it out. Or we email them asking for more detail on what wanted or where they found what they were looking for.
In both cases we update the 'best bets' and synonyms links that show up in the search results - so that if the same search is done again there is something to help the searcher.
Success
This personal approach has been phenominally successful in improving staff confidence in the search tool, and have happy huggy feelings for the intranet.
Hope this helps
Dorje
For more intranet information those of us Down Under share information here via
http://onlinegroups.net/groups/kiwi_intranets