I operate on the assumption that my credit card number has already been stolen and distributed on countless lists on the internet, and it's just a matter of time before someone tries to buy something with it. This doesn't bother me, because I check my credit card account every 2-3 days and quickly see any fraudulent charges. When this happens (has been 2-3 times in the past decade), I call the bank, they reverse the charge, and send me a card with a new number. No inconvenience to me except for an unnecessary phone call. (I'm much more worried about identity theft in the form of someone opening a new line of credit that I have no easy opportunity to review or check, other than checking my credit three times per year).
So, I just cut my old cards into three pieces and put them in different wastepaper baskets in my house. If someone is enterprising enough to open all of the bags in my apartment complex dumpster, sort through them, put the number together, and then make a single purchase (at which time I will see it and report it and not have to pay for it), well ... maybe they deserve that random thing they bought, I guess.