Question about shutter speeds

I have a MiniDV Canon camcorder and was wondering about shutter speeds, it has speeds from 1/60 to 1/2000, what would be the reasons for switching speeds? If you have a slower speed it lets more light in so would say 1/60 be set for low light scenes? How would this affect motion?

 

The slower your shutter speed, the longer it will let light in. As a result of that longevity, you will have more motion blur. So the higher the shutter speed, the more crisp and jittery your video will look. I shot a duel recently on the FX1 and we shot at 1/10,000th. We wanted to go as high as we could without starting to lose a bunch of light. Luckily for our camera settings, it was insanely hot and sunny...not so peachy for us though

 

Adding to what DMP said:
With slower shutter speeds you get a kind of blurring effect which can be of use in dream sequences. Faster shutter speeds like 1/250 or 1/500 produce the crisp images seen in war movies like Saving Private Ryan or in fightscenes of Gladiator.
When creating slomotion footage from your 60i original you should use a shutter of 1/120 to get the right amount of motion blur. Otherwise your slowed down footage will look too soft and blurred.