Hinge for mounting a door on a piece of furniture or the like, comprising: a hinge arm having a first and a second side walls (11"), the hinge arm being fixable to a fixed part or to a door of the piece of furniture; a box fixable to the door or to the fixed part of the piece of furniture and connected to the hinge arm by an articulation system comprising a plurality of movable connecting levers (16, 18, 20, 23) and seven articulation axes (17, 19, 21, 22, 24, 25, 26); spring means acting in closing direction of the hinge; and a damping device having an actuation member linearly movable according to a longitudinal axis, said damping device being at least partially enclosed between said side walls (11") of the hinge arm, and wherein the actuation member of said damping device extends at a front end of the hinge arm facing the hinge box for contacting a thrust element of one of said connecting levers (16, 18, 20, 23) of the articulation system or integral with one of the same levers (16, 18, 20, 23) or with said hinge box at least in a range near the closing position of the hinge, wherein the hinge arm comprises a housing seat (32, 41) for said damping device, open at least at the front end of the same arm, the damping device being fitted in said housing seat (32, 41) and wherein said housing seat is conformed as a cavity made in an intermediate wall between said side walls of said hinge arm, characterized in that the damping device has a housing body conformed to be arranged and fixed in said housing seat in a removable way; said housing body comprising quick fixing means for fixing and releasing the damping device to the hinge arm in order to hook and unhook said damping device with respect to the hinge arm in a simple manner. a hinge arm having a first and a second side walls (11"), the hinge arm being fixable to a fixed part or to a door of the piece of furniture; a box fixable to the door or to the fixed part of the piece of furniture and connected to the hinge arm by an articulation system comprising a plurality of movable connecting levers (16, 18, 20, 23) and seven articulation axes (17, 19, 21, 22, 24, 25, 26); spring means acting in closing direction of the hinge; and a damping device having an actuation member linearly movable according to a longitudinal axis, said damping device being at least partially enclosed between said side walls (11") of the hinge arm, and wherein the actuation member of said damping device extends at a front end of the hinge arm facing the hinge box for contacting a thrust element of one of said connecting levers (16, 18, 20, 23) of the articulation system or integral with one of the same levers (16, 18, 20, 23) or with said hinge box at least in a range near the closing position of the hinge, wherein the hinge arm comprises a housing seat (32, 41) for said damping device, open at least at the front end of the same arm, the damping device being fitted in said housing seat (32, 41) and wherein said housing seat is conformed as a cavity made in an intermediate wall between said side walls of said hinge arm, characterized in that the damping device has a housing body conformed to be arranged and fixed in said housing seat in a removable way; said housing body comprising quick fixing means for fixing and releasing the damping device to the hinge arm in order to hook and unhook said damping device with respect to the hinge arm in a simple manner.