The early "movie industry" spent lots of time and money looking for a way to make the stagecoach wheels go the right way, and eventually figured out that most people just accept it and it doesn't really matter "artistically."
The name usually applied to phenomena of this sort is "strobe effect." Many record turntables have/had a circle of bars marked on the periphery of the platter, with a small neon light illuminating them. Since neon on ac power actually extinguishes and relights every time the voltage goes through zero, you get a light that flashes at 2x the line frequency - 120 Hz for US 60 cycle, or 100 Hz for Brit 50 cycle power.
If the "next bar" has moved exactly to the position of the previous one when the light comes back on, you see a stationary pattern, and theoretically your platter is turning at proper speed.
If the "next bar" has moved past the where the previous one was, the perceived pattern will rotate in a forward direction, and the platter is turning too fast.
If the "next bar" doesn't quite make it to where the previous one was, the pattern will appear to rotate "backwards" - like the stagecoach wheels - and the turntable is going too slow.
In the case of the stagecoach, if you watch very closely as a coach in a movie starts up, you will see a "flash" instant where the spokes appear to stop rotating in the "correct direction," but the coach will appear to have twice as many spokes as are really there. This happens when a spoke moves exactly half-way to where the preceding spoke was, so that at the second succeeding frame it's also seen in the same place where the preceding spoke was two frames earlier. This is also the instant at which the "apparent rotation" first reverses and it begins to look like the wheel is turning backwards. For a typical rear stagecoach wheel 40 inches in diameter (variable) with 18 spokes (pretty standard) this will happen, for a 24 frame per second camera, at about 5 mph - a brisk waking speed (about 3 mph for a 36 frame/sec camera). As the coach speeds up, the "apparent rotation" will be first forward, then backward, then forward, then.... Unfortunately you have to double the speed to get from where the last "backward phase" starts to where the motion next reverses, so for "high speed runaways" you'd need a 90 mph stagecoach to see the wheels go the right way (or 8 foot diameter wheels).
For the worms that Wolfgang provided, the "stobe effect" is provided by what's called the "saccadic motion" of your eyeballs, which is another story. Suffice it to say that frogs can't see the worms move.