UPDATE: Well, that'll teach me to blog about physics I don't fully understand! I have researched the issue and edited the post below, now that I understand the explanation from The Straight Dope.
Last night the Discovery show Mythbusters settled a longstanding debate: whether an airplane on a conveyor belt (running in the opposite direction as the plane) can take off. The short answer, as liveblogged by Jason Kottke:
HELL YEAH THE PLANE TAKES OFF
It's a curious problem. As a thought experiment, it seems (at least to me) like the plane shouldn't take off, since it wouldn't gain takeoff velocity relative to the ground. But according to, you know, SCIENCE, the plane will still reach takeoff velocity -- the wheels will just spin twice as fast. This is because the wheels aren't providing any thrust, it's the engines (propellors) that are pulling the plane forward through the air. It's the velocity of the air relative to the wings that counts, which is generated by the action of the engines pulling the plane forward. So the conveyor belt will only stop the plane from gaining takeoff velocity if it creates enough friction to counteract the forward thrust of the engines (or propellor).
Despite explanations of this sort by physicists, the issue wasn't really settled until last night's Mythbusters episode -- they replicated the experiment on a small scale, then with a real airplane (albeit an ultralight), using a huge tarp dragged by a truck as the "conveyor belt." Even the plane's pilot thought the plane wouldn't overcome the power of the conveyor belt, and thus wouldn't gain takeoff velocity. When Jason Kottke first blogged about the issue last February, his comment thread was hot with controversy. So Kottke tuned in to Mythbusters last night and liveblogged the event, with results visible above. His exuberance over the plane's liftoff has resulted in a "HELL YEAH THE PLANE TAKES OFF" tee-shirt available starting at $18. Wow.
Watch the Mythbusters clip in question below.... (Note: if this clip is pulled down, I'll try to dig up another.)
Keep in mind that the issue here is partly semantic, and has to do with how you explain the theoretical problem. I explained it poorly in my first post, since I (like apparently many) assumed that air would flow over the wings as a result of the propellor spinning, and that would be enough to make the plane take off, even if it was stationary. This is not the case -- the plane is going to need to move air over its wings in order to take off. The point of the experiment is simply that yes, the plane will move despite the conveyer belt underneath it. And that movement (at least in this experiment) provided sufficient lift to get the plane off the ground.