Can a ceiling fan's speed be controlled with a light dimmer switch
Light dimmers use triac based phase control for dimming purpose. It chops the sine wave somewhere in between depending upon the knob position, which produces a signal like this:



(a) is pure sine wave. (b) and (c) represent modified sine wave going to the appliance depending upon dimmer knob position. This works well for dimming an incandescent bulb because they give off light based on heating of the filament. 

However when you give this waveform to a ceiling fan, it won't behave very well. Most obvious issue will be a humming sound specially at a lower speed (corresponding to signal (b)). Lesser obvious issues might be increased energy loss in the coil.

Nowadays companies have started using a series capacitor to reduce the voltage while maintaining a sine wave which eliminates humming while reducing the fan speed.