By far the most common is the aforementioned automotive damper. This simply works by applying a retarding force to the crank which tends to lower the magnitude of its acceleration and decceleration. Note that you cannot do this with a rigidly coupled device, such as a flywheel. You must have an elastic coupling between the crankshaft and the damping weight. The automotive damper takes the vibratory energy of the crankshaft and dissipates it as heat.
Aircraft engines use a sarazin or chilton type pendulous damper.
This device stores the acceleration of the crankshaft as potential kinetic energy and forwards it back into the crankshaft when the crank starts to deccelerate. It accomplishes the same thing that the automotive damper does but it uses a different principle. It also does not remove energy from the engine - hence it does not heat up. Instead of dissipating torsional vibration as heat, it stores it and returns it to the crank. Now torsional vibration is probably the MOST vexing problem associated with reciprocating engines.