My own parents think they are safe, because they carry no credit cards and only use a savings account to pay bills.
Actually, they are somewhat safer. A couple of years back I read most ID theft (something like 70%) is still done the old-fashioned way (manually): lifted creditcard numbers from signed receipts and stolen mail being two of the favs. I wouldn't be surprised by some shift in those stats though.

I keep thinking about a retired CIA-man I met at a reception back in '01. Said he wouldn't touch a computer with a ten-foot pole. If he stays awake at night, at least it's not from something he did on a PC.

I still much prefer paying cashola whenever possible. I find it fascinating that consumers feel safer in a cashless society in which fraud and robbery (albeit in a different form) have become a surer prospect.