The Danes have their own local debit card: the "Dankort", which totally dominates the market and is highly loved by the locals because the government-regulated fees are low, but disliked by anyone else, since it makes the acceptance of VISA/MC so low and expensive. How this can be compatible with the SEPA (Single European Payment Area) rules is something I have never understood.

My workaround is to use cash withdrawn with a Swedish debit card that has no ATM fee.