Annotated Mythbusters

The aircraft will still take off. Unlike our cars, airplanes are not powered by it's wheels.

That plane is going nowhere! It doesn't matter that the engine moves the air trough itself - what makes a plane to take off is the air moving around its wings; if the plane is stationary to the air it will never take off and the engine suction will never create enough draught around the wings to generate any lifting force.

The only problem with that argument is that the tires will explode before the plane hits the required speed and crash into the ground.

Notice that the setup never tells you what speed of the plane to use. I take that as an open door for both theorectical and practical approaches.
Obviously if you use the plane's airspeed or ground speed the plane will take off.
Now if you use the plane's rolling speed, which is relative to the belt, then the plane can't theorectically take-off, just based off the matched speeds. Practically this can never occur unless the plane is at rest.

First of all, the plane will not lift off! Any fixed wing plane, prop driven or jet, has to have air speed in order to lift off. Relative to the ground (or plane), there is no air speed in this experiment. It's very simple; not even worth arguing.

Secondly, the tires/wheels have nothing to do with the problem. Imagine that the conveyor is ice-covered and the plane is on skates. Same result: no lift-off

Two things required to takeoff... lift greater than weight, thrust greater than drag. They are fully independent in this case. Mythbusters will find that thrust can be greater than drag and the aircraft will accelerate with respect to the belt. However, lift is equal to 0.5 * air density * velocity(squared). The velocity is that of the freestream air which is zero here. Therefore, no lift and no flight.

I just watched this one... What I find appalling is that the pilot was surprised that the plane took off. All these comments saying how the plane can't take off have to be coming from people who've never taken a basic physics class. The fact that the pilot was shocked (his word) tells me that he really doesn't understand the physics required to fly, so he really shouldn't be flying.