On the BMX bike I have, pedaling backwards moves the chain but doesn't drive the wheels of the bike backwards like you would expect it to. Why is this?
Do you hear a "tick" sound every time you spin the wheel anti-clockwise? that's the freewheel mechanism composed by two small parts called "pawls" and when you spin it on that direction, those pawls turn loosely until they find the "dent" in the inner mechanism (the ratchet body), that's when the "tick" sound happens.
When you ride your bike, those two pawls do exactly the opposite, they catch the "dents" and force the inner mechanism to rotate! it's wonderfully ingenious and simple at the same time.
I've disassembled and assembled several and it amazes me every time.
The freewheel allows forward pedalling to lock and drive the bike, but spins freely when reversed.
Some BMX style bikes (and kids bikes) have coaster brakes, where if you pedal backwards (well usually they do not actually pedal backwards, just the motion is begun) and it brakes the bike.
I remember well locking the back wheel and trying to generate skid marks on the sidewalk.