There's no reason a store should 'want to see them' if you present the card. My advice is to copy the numbers someplace secure for you, then erase them off of the card (nail polish remover). Without them it is very hard to order online. Also do not sign your card, but write "Request Photo ID" and protect yourself from illicit charges. Just make sure you carry your Driver's License with you. Erasing the security code will prevent a friendly waiter from copying all the numbers down and using them later....don't ask.
On an aside, one of the local shops was recently busted and cleaned out by a paddy wagon. They would take in peoples cars, and make copies of all the keys on their key rings while 'test driving' the car. They have home addresses on work orders. So far, cops have tagged the group of employees (11) with 42 home burgalries, 109 stolen cars and 11 'hot' home invasions (when owners were present) over 7 years. Nice. One more reason to work on your own car, or not let it out of your sight while being serviced.
When I have to leave a car, I leave the one ignition key and notate the mileage. Friggin' thieves.
