In an MSN.com article a few weeks back they said something very interesting - one of the things that determine the credit rating is how much of your total available credit you use, so if people already have a credit card they should pay it off, but not close it as it would lower your total available credit. If people start closing all sorts of paid off accounts it will actually hurt the credit rating. I guess, technically, you could still cut up a CC, just dont close it
All of this is from vaque memory - I am sure a search for the article would reveal more info.