Payments amounting to several thousand pounds were charged to my card and credited to a Virgin mobile 'Pay as you go' account that had been opened in my name. The Virgin system picked up abnormally high amounts being credited to the account over a period of about two weeks and they contacted me. I had no knowledge of what had been happening, but my card provider immediately froze my card account and set me up with a new one.
It happens more often than you think, although it will be far more difficult with chip and PIN cards. There will be no slip with your PIN on it, so nobody can charge to your account, even if they have all the details from the original card, or the card itself.