I would always switch doors.
This is my reasoning. If you don't switch doors, then you have a 50% chance of getting the car. (Actually, it's only 1/3, but when the other goat is revealed then I know I at least have a 50-50 shot that my door hides the car.) However, if you switch doors, then you have a 67% percent chance of getting the car.
If you switch doors, there are only three outcomes possible, and 2 of the 3 result in you getting the car.
1: you picked a goat. Goat revealed. You switch and get the car.
2: you picked the other goat. Goat revealed. You switch and get the car.
3: you (were unlucky enough to have) picked the car. Goat revealed. You switch and get the goat.
At the get-go, what are you more likely to pick - a goat or a car? Well, your odds are 2/3 for a goat and only 1/3 for a car. By switching your pick after a goat is revealed, you get to flip those odds in your favor: 2/3 of the time you'll get the car and only 1/3 will you switch and get a goat.
This is what I tried to explain to my friend, who, by all accounts, is a highly intelligent, very accomplished individual. (He has a doctorate in psychology and a law degree as well.) However, he was having none of it, and argued vehemently that there was no statistical advantage to switching.