There’s a neat article  in the September-October 2008 issue of American Scientist (although sadly, this particular article seems not to be online) in which Brian Hayes discusses the Monty Hall problem and people’s strong resistance to the official solution to it.
Now, folks like Jason have discussed the actual puzzle about probabilities in great detail (on numerous occasions). It’s a cool problem, I believe the official solution, and I’m not personally inclined to raise skeptical doubts about it. What I really like about Hayes’s article is how he connects it to the larger ongoing discussion in which scientists engage:
The issue that concerns me here is not who is right and who is wrong about the odds of winning on Let’s Make a Deal. The issue is how I can persuade anyone that my answer — or any particular answer — is correct. I have been stewing about this for several weeks, frustrated that I am powerless to communicate what i take to be a simple truth. But I’ve finally decided that what the episode demonstrates is the vigorous good health of the scientific enterprise.
Making progress in the sciences requires that we reach agreement about answers to questions, and then move on. Endless debate (think of global warming) is fruitless debate. In the Monty Hall case, this social process has actually worked quite well. A consensus has indeed been reached; the mathematical community at large has made up its mind and considers the matter settled. But consensus is not the same as unanimity, and dissenters should not be stifled. The fact is, when it comes to matters like Monty Hall, I’m not sufficiently skeptical. I know what answer I’m supposed to get, and I allow that to bias my thinking. It should be welcome news that a few others are willing to think for themselves and challenge the received doctrine. Even though they’re wrong.
Very well put. One hopes, in the ongoing conversations, that all the parties prioritize the truth over their own biases and intuitions.
 Brian Hayes, “Monty Hall Redux,” American Scientist (September-October 2008) Vol. 96, No. 5, 434-435.