As others have stated, no reason not to let them have a quick look, but certainly don't let them make a copy of the drivers license.

Have you noticed some retailers are also asking for ID when you purchase with a credit card? It doesn't seem unreasonable to at least make an effort to verify the person giving you a credit card is the person whose name is on it. Anyone can fudge a signature on a little credit card slip. It's not only for their protection, but for that of someone whose credit card has been lost or stolen. I know you can make the arguement the card should be reported stolen immediately, but it's a fact that people in possesion of lost/stolen cards can rack up LOTS of charges fast before that will prevent them from using them.