When does the wagon-wheel effect occur? Sometimes you see a video of a fan or a propeller spinning very fast, and the apparent rotation is distorted. The fan can appear to be moving in the opposite direction of rotation, or even stationary. This optical illusion is known as the wagon-wheel effect. If I understand correctly, this occurs because the camera framerate is slower than the frequency at which the fan makes one rev, so stroboscopic effects should be expected. 
Does the wagon-wheel effect occur only in videos, or can we observe it just with the eye?
 A: There are three frequencies here, two frequencies $ f_1,f_2 $ are nearby to each other  and the third human eye capability frequency $ f_E$. Stroboscopic effects occur is when $ |f_1-f_2| < f_E $. Thus if they are spinning at 5000 Hz and 5002 Hz when human eye cannot detect more than say 30 Hz,stroboscopic wagon wheel effects are still seen. 
A: The simple answer is yes, you can see it with the naked eye. It requires only that the light source is showing significant, periodic variations in intensity, and preferably with a frequency greater than the fusion frequency of the human eye (20 - 30 Hz).
The greater the intensity variation, and the shorter the "on" duration, the more pronounced the effect will be. Under some circumstances you can even use fluorescent lighting.
It used to be a common technique to use a strobe light to analyze rotating machinery, although I expect that video cameras are more common these days. If you're actually interested in messing around with this, you can go on eBay and get a working Strobotac for less than $100. This produces a beam of flashing light, with the flash frequency variable to suit the object you're looking at. Shining this on any rotating object can produce interesting results. Or, if you're handy with electronics, you can save some money and make a driver for some high-power LEDs (not white) and get useful results, although strobe tubes give higher peak light levels and so are easier to use.
A: From my experience it also occurs when objects spin at a faster rate than our eyes can perceive them to. I see it all the time on wheels of vehicles on highways and all, and also for fans, of course. 
