As a new Nikonian, I'll contribute.
The answer is simple - you need a fast shutter speed to stop the ceiling fan.
That's it...lesson over.
OK, maybe you knew that. So let's talk about how to get a fast shutter speed. Exposure 101 - there are three things that contribute to exposure: shutter speed, aperture, and ISO. Using a combination of these you (or the camera) make a decision on how much light will hit the sensor and make the image.
For many scenes, you can choose any combination of shutter speed/aperture/ISO to get proper exposure, but when you are trying to stop a moving object, you have to have a fast shutter speed. So that means you have to get enough light to the sensor using a combination of aperture and ISO.
The more light you can get to the sensor using aperture and ISO, the faster your SS can be.
Lets start with aperture. I took the following images of my ceiling fan at its highest setting using different aperture/shutter speed cominations to make the same exposure (Nikon D80, Nikon 50 f1.8 lens):
f5.6 aperture required a 1/125 shutter speed. Not fast enough.
f4 aperture required a 1/250 shutter speed. Not fast enough.
f2.8 aperture required a 1/500 shutter speed. Almost fast enough.
f1.8 aperture required a 1/1000 shutter speed. Finally fast enough. Bad focus do to shallower depth of focus at f1.8 - everything's a tradeoff!
So by opening up my aperture I was able to let more light in, allowing me to use faster shutter speeds.
That's why fast glass is so important to sports shooters. It's also a lot more expensive, and usually a lot bigger and heavier.
But what if your lens only opens up to f4 (like the kit lens)? You still need to get more light to the sensor in order to be able to use a faster shutter speed. You can do this by bumping up your ISO. Using just the ISO I can achieve the same results as above:
f5.6 aperture requires a 1/125 shutter speed at ISO100. Not fast enough.
f5.6 aperture required a 1/250 shutter speed at ISO200. Not fast enough.
f5.6 aperture required a 1/500 shutter speed at ISO400. Almost fast enough.
f5.6 aperture required a 1/1000 shutter speed at ISO1600. Finally fast enough.
Bottom line is to use the combination of aperture and ISO to stop the motion. Buying an f2.8 telephoto will really help get the fast shutter speeds!
Of course. you can also stop motion with your flash:

(ISO 100, f5.6, 1/125)
But that's a topic for another thread...