My mathematical training says you're indifferent, that the probability is 50/50 you'll get the car behind either Door 1 or 2. But I'm wrong, and the implications are poor for a number of psychological experiments performed in the past 50 years.
Follow the first link for the real probability, and try your hand at the game itself here.
Update: as reader rick reveals, it's all about timing:
in fact, monty reveals the goat *after* we made our initial choice. that is, that goat was relevant to our first choice.
in particular, when we made the first choice, what was the chance of picking the sports car? answer: 1/3
thus there was a 2/3 chance that the car was behind one of the two remaining doors.
which of those two doors? we don't know unless somebody shows us...
