SOFORT banking is a very nice and convenient payment system inside the European Union, which appears to charge vendors less than credit cards and Paypal do, and the cost savings are passed on to the customer. AFAIK you don't enter your banking details to a web page run by the vendor, but actually into some web frame provided by SOFORT, so you as customer, get all the safety features and precautions of an established payment processo. The webshop just get a confirmation code after the transaction is complete, and never sees your banking details.
I would be quite surprised if this worked with bank accounts outside the EU.