nobody's mentioned this -- some credit card companies let you generate a 1-time use credit card number with a credit limit you can set yourself. So if you want to buy something online, you go to Citibank or somewhere first and generate a number, set a limit of $100, specify that the card expires in a week or something, and bingo! Discover does it too, probably others.

it is almost not worth bothering for credit cards, though, because I think they pretty much all have fraud protection now.

personally, i think paper statements have their own drawbacks (can get stolen from your mailbox, have to shred them, etc). also i would never, never use a debit card online, because it's a direct line to your bank account. I know there's fraud protections there too but I personally find it a lot scarier to imagine less money in my bank account than some weird credit card bill I know I don't have to pay.

and i have OCD so believe me I've thought this through.