This is a very tantalizing puzzle. At the outset it is very difficult to see why the odds should be different than 50-50. Thanks to everyone who responded, and there were many who did.
The answer goes as follows:
Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance. One way to see this is to notice that there is a 2/3 chance that the initial choice of the player is a door hiding a goat. When that is the case, the host is forced to open the other goat door, and the remaining closed door hides the car. “Switching” only fails to give the car when the player had initially picked the door hiding the car, which only happens one third of the time.
If one would like a detailed discussion on this puzzle as this one has baffled mathematicians for a while, please go to: http://en.wikipedia.org/wiki/Monty_Hall_problem
Hope you enjoyed this!