Berj A. Doudian writes in to Cecil at The Straight Dope:
Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words “airplane” or “conveyor belt” everyone starts right back up. Here’s the original problem essentially as it was posed to us: “A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed [relative to the still ground next to the runway] and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”
Answer here.