It depends on the type of restaurant. Table-service restaurants generally do not require payment in advance [if you look like you can pay]. Take-out, delivery, and counter-service restaurants generally require payment in full before fulfilling your order. Buffet restaurants are split: some require payment as you walk in the door, and others require payment on your way out.

This leads to the somewhat paradoxical situation where you cannot buy a hot dog on credit, but you can get a porterhouse, lobster tail, salad, baked potato, and a beer and not be expected to pay until well after the food is already beyond recovery.