I've heard stories like "fine, we'll take your debit card, but only if you also pay a non-reimboursable $$$ deposit in cash" for car rental. (Mostly in central/eastern Europe.)

(From what I was told, the thing in favor of a credit card is that the rental agency can put a hold on the security deposit for much longer than on a debit card: a few weeks vs a few days).

Custom in Europe - where debit cards are the most common - is to settle the hotel bill on check-in.

Obviously. Because why would a rental company turn down > 90% of the customers?