Yes, some car rental companies in the US accept debit cards, under special conditions and requiring additional documents, such as utility bills, proof of resources, proof of insurance, extra identification documents. Make sure to contact the agency to be aware of the conditions. In most European countries, it is also possible to pay with debit cards, but it is advisable to check on a case-by-case basis by contacting the rental company. If you wish to pay for your rental by debit card, prepaid card, cash, vacation vouchers or bank check, you will be asked to make a deposit and/or take out specific insurance.