What is the name of an apparatus fixed to the wheels of a car to lessen the effects of rough road surfaces?
The short answer is "shock absorbers". But, there is much more to a car's suspension to reduce the effects of rough road surfaces than simply putting in shock absorbers. The primary purpose of suspension systems in cars is to ensure that the tires maintain contact with the road surface. The nice ride for the passenger is an added bonus.
You have the vertical shock absorber which transfers the energy from a bump in the road into a spring or hydraulic piston rather than to the frame of the car. Having shock absorbers in proper working order will ensure that the tires do not lose contact with the surface of the road or give the passengers a horrible rough ride over moderately rough roads. Some cars use struts which function as shock absorbers and also carry some of the weight of the suspension as well.
The second component that increases tire contact with the road and reduces side-to-side motion of the vehicle is anti-sway bars. Most modern cars are equipped with these devices which eliminate the roll that many experience when making a tight fast corner. In extreme cases, the tires may actually lose contact with the road surface causing a danger to driver and passengers