Most hotels out there accept cash. However, not all of them do. So please make sure, when you check-in that you ask the front desk to pay by cash, so that they do not charge your credit card. This only applies to free cancellation bookings.
You might be able to leave a deposit in cash instead of a hold on your credit card for incidentals. So make sure you warn the front desk that you want to pay by cash for all or part of the transaction.