Headgear is provided having one or more electrical devices, such as light sources mounted thereto. The headgear includes a power source for providing power to the electrical devices and a motion sensing device, such that any operating electrical devices are shut off if the hat does not move within a predetermined time period to conserve the life of the power source. In one form, the motion sensing device is operable to reset a shut-off timer when movement of the headgear is detected by the motion sensor so that the light sources, for example, are not turned off when the headgear is worn with the light sources turned on. In this manner, the shut-off timer is constantly being reset when the headgear is worn to keep the shut-off timer from timing out and turning the light sources off.