They usually have to be 'activated' first, which gives card vendors the opportunity to collect your information before allowing purchases. This isnt common practice yet, but I'd bet that's coming. Even if they don't collect your pre-activation info, the date, time and place of purchase are recorded and attached to the card. It wouldn't be a stretch for law enforcement to request CC/security video from the merchant at the date and time of purchase. So I don't think they offer as much privacy as cash unfortunately.