Yes, but the Visa and Mastercard merchant agreements say that merchants are not allowed to refuse service if you don't provide identification, and their websites include problem-report forms for merchants who refuse service because you don't have ID.Technically, merchants are supposed to ask for your ID when you use a credit card to verify you are an authorized user of the card, but none of them ever do.
Since the merchant isn't allowed to refuse service upon failure to produce ID, most of them don't even have the employees ask - not due to laziness, but due to there being basically no upside to doing it.