As mcparadise stated, the parking brake should always be used–with one possible exception–in addition to placing the transmission in the “park” position.
The exception to the rule is if you have been driving in wet weather and the temperature is predicted to drop below freezing. In that case, the parking brake should not be applied, as it could freeze in the “on” position, thus making it impossible to move the car the next morning.
However, bear in mind that if you are parked on glare ice, nothing is going to prevent the vehicle from sliding. The combination of a slope and ice is an indication that you should park elsewhere!