Why? Even if someone stores your number and uses it fraudulently, most (all?) credit card companies will reverse the charges that you didn't approve.

Care to share a few of your credit card numbers?

I actually thought about dropping my AMEX number just for giggles, but intentionally exposing it would probably invalidate their guarantee.

It's still a hassle though. Dealing with fraud and replacing your card is something I imagine most people would rather avoid having to do.