Can someone explain to me how it is that an incandescent dimmer will make a fan hum and ruin the motor, but a fan controller will not? How does the fan control accomplish speed control without ruining the fan motor?

Also, how does a low voltage (transformer)dimmer differ from an incandescent dimmer? I have seen low voltage transformers fail on an incandescent dimmer, but I don't know why.

Well I will give this my best shot.

Most modern incandescent dimmers use a Triac that switches off every time the Sine wave reaches 0 volts, and then "turns back on" at some point in the wave according to where the dimmer is set.
More dimming = more of the sine wave being "chopped" out.
Less dimming = less of the sine wave being "chopped" out.
So that being said you can imagine what the sine wave would look like on an "O"Scope with this type of dimmer. Light bulbs being a resistive load it really doesn't matter what the sine wave looks like.

Inductive loads however really like a nice sine wave or they tend to become very inefficient which in turn causes heating which can lead to failure.

I am not exactly sure of what a fan controller is made up of (maybe a triac and caps to smooth out the sine wave?) but I do know that they don't "mess" up the sine wave near as much as a incandescent dimmer does.

Hope this explains things, and if my explanation isn't 100% correct I hope someone here will help me out and correct me.

Another thing with all the fan controllers that I've seen is that they have a small trimming potentiometer which you set so that you can't stall the fan when it's turned to the lowest speed. Dimmers don't have these.

As for low voltage dimmers, I was told that they are just a higher quality dimmer capable of handling magnetic (transformer) loads.