Yes! The key to this problem is that the host is predestined to open a door with a goat. He knows which door has the car, so regardless of which doors the players pick, he always can reveal a goat first. The question is known as the "Monty Hall Paradox." Much of the confussion about it is because often when the question is framed, it is incorrectly not made clear the host knows where the car is, and always reveals a goat first. I think put some of the blame on Marilyn Vos Savant, who framed the question badly in her column. Let’s assume that the prize is behind door 1. Following are what would happen if the player (the second contestant) had a strategy of not switching.
Player picks door 1 --> player wins
Player picks door 2 --> player loses
Player picks door 3 --> player loses
Following are what would happen if the player had a strategy of switching.
Player picks door 1 --> Host reveals goat behind door 2 or 3 --> player switches to other door --> player loses
Player picks door 2 --> Host reveals goat behind door 3 --> player switches to door 1 --> player wins
Player picks door 3 --> Host reveals goat behind door 2 --> player switches to door 1 --> player wins
So by not switching the player has 1/3 chance of winning. By switching the player has a 2/3 chance of winning. So the player should definitely switch.
For further reading on the Monty Hall paradox, I recommend the article at Wikipedia.