The question: Do the odds of you getting the car increase if you switch? Or is it 50%, so it doesn't matter if you switch or not?
The puzzle is actually a very famous one. In 1990, Marilyn vos Savant published her answer to the puzzle in her newspaper columm and immediately got thousands of letters claiming she was wrong, some of which were PHD holders and professional mathematicians.
Anyway I got this puzzle from a book I am reading now called "the curious incident of the dog in the night-time" by mark haddon, a story about an autistic teenager with amazing memory and logic skills who tries to solve the murder of his neighbour's dog in the style of his favourite detective, Sherlock Holmes. It's quite an amazing read so far, highly recommended.
Update: The answer (this is for you, Frankie):
/ | \
G1 G2 C
S/ \NS S/ \NS S/ \NS <--- 2nd choice after Host reveals one goat
C G1 C G2 GX C
G1 - Goat 1
G2 - Goat 2
GX - Either Goat
C - Car
S - Switch
NS - Not Switch
As you can see from all the possible outcomes in the badly illustrated diagram, you get 2 out of 3 chances to get a car when you switch, and only 1 out of 3 chances when you don't.