Probability 101: Monty Hall

Many of you know this already, so hold off for a minute (or a day) and let folks who have never heard it try to reason it out. I'll try to give a complete and clear explanation to start with...

You are a contestant on Let's Make a Deal. You are given the opportunity to choose one of three doors - behind one is the Big Prize, behind the other two are goats. Assume that you want the Big Prize, and don't want a goat...

You choose a door but, before Monty shows you if you've won, he opens one of the doors that you *didn't* choose, revealing a goat. He then gives you the option of staying with the door you originally chose, or switching to the last remaining door (the one you didn't choose and that he didn't open). What should you do?

Caveat: This a pure probability question; assume that there is no way to gain any more information about what is behind either door. You must make your choice based only on the information provided.