I know at least a couple of European countries where debit/credit cards are prevalent.
In Finland it seems that absolutely everywhere accepts card and cash is very rare. I'd guess at least 95% of the in-person transactions that I see are made with card. Even for the smallest amounts.
For instance, I can buy milk at £0.49 on an American Express card in Tesco, but in my local pub, anything under £10 (on any card other than AmEx - AmEx is still not accepted in that many places in the UK) requires me to pay a £1 transaction fee.
There is no reason behind this, other than Tesco are so huge, they can negotiate a much better rate than a small business, who clearly can't even consider the huge American Express merchant fees.
The sooner somebody disrupts this 'business', the better for everyone.
IE, your choice of supermarket is more elastic than your choice of pub.
Bitcoin seems to be the closest thing we have to disrupting this, but the chicken and egg problem isn't going anywhere.
Actually, I believe handling cash costs them money too and card processing fees might be less than what cash costs them.
It's interesting to compare with the situation in China, where credit cards are very rarely used, but I've never had a problem paying with one in any kind of decently-sized store or restaurant. You almost get the impression that they knew you were coming and set aside a card machine just for you.