A machine (1) for making and dispensing frozen food products such as crushed-ice drinks, sorbets and the like comprises a tank (3) for containing and processing the product to be dispensed and a tap (4) whose dispensing duct (17) is connected to a discharge hole (15) which is made in the front wall (10) of the tank (3) the tap (4) in turn comprises a plug (19), able to move between a position (A) in which the duct (17) is open, allowing the product to be dispensed through the duct (17), and a position (C) in which the duct (17) is closed, preventing the product from coming out through the duct (17) when the plug (19) is in the closed position (C) it is coaxially inserted in a sealed fashion in a cylindrical tubular portion (17a) of the duct (17) extending longitudinally starting from the discharge hole (15) in a direction at a right angle to the front wall (10) of the tank (3).