A device for braking the movement of a movable member with respect to a support structure includes a casing fixable to the movable member or to the structure and defining a chamber containing a viscous braking fluid, and a rotor, operationally associable with the movable member or with the structure, and which is rotatably connected to the casing and is mounted thereon so as to close the chamber. The rotor includes a piston-like member or portion, mounted so as to slide within the chamber in such a way as to separate the chamber into separate regions in mutual fluid communication. The piston-like member or portion is movable integrally with the rotor, such that rotation of the rotor brings about a rotatory displacement of the piston-lie member or portion, braked by the resistance to the passage of the fluid from one region to the other of the chamber caused by the displacement of the piston-like member or portion.