In this question comments raised the question of whether or not it could harm an engine if it was forced to turn in the "wrong" direction – for example if a car is parked on a hill pointing uphill and left in first gear, could damage be done if it rolled down the hill?
I would imagine that this is specific to the engine and transmission as some can do this with no obvious harm – for example old SAAB two-stroke engines would run in either direction depending on the ignition timing (and it seemed the phase of the moon) and direct reversing marine engines which "shift" into reverse by stopping, moving the camshaft, and restarting.
So, if there are potential problems, what components are involved and how would someone know if there is a risk of damage?