I’ve just caught the end of a TV ad for a Capital One credit card; it includes one man advising his mate to “then cut it up into little pieces and get a capital one card instead”. I really wish people would move away from the idea that cutting up a credit card is the be-all-and-end-all solution. Yes, of course it stops you spending on it (though not if you still have the number, as then you can still spend on the web or phone); but at some stage you’ll be sent a new one.
The key, if you’re not going to use a card again, is to cancel it (having of course balance transferred the debt away), this really does close the card, it also improves your credit score in the long run (see should I cancel old credit cards article).