[Pat McCarthy]

The Mythbusters have conclusively proven that a plane on a treadmill can take off! (When comparing airspeed vs. conveyor speed)

Warning! Science Content!
This can be explained by comparing the means of propulsion of a plane vs. a car. A car uses the powered spin of its wheels to propel it forward.

Now a plane uses it's propeller to push against the air, while the wheels are left to free spin. And a plane depends on the speed of the air passing over its wings to generate lift to take off. With enough headwind, a plane can take off while not moving relative to the ground. Thus, a plane will pull itself through the air, no matter if it's wheels are spinning (or how fast they are spinning) or even if they are not spinning at all.

There is a corollary to this.
And I'm not sure if I will be explaining it right.
You have to be measuring the plane's airspeed for the experiment to work. If the speed of the wheels was monitored, and you were only trying to match the speed of the conveyor belt to the rotation of the wheels, assuming no friction in the system other than that between the wheels and the conveyor, the plane wouldn't have to exert any propulsion of any kind to remain stationary (Newton's First Law of Motion). However, in real life, the plane would be pulled backwards along with the conveyor, relative to the ground due to the friction of the wheels and their bearings. So to counter this, the plane would have to be pushing some air with its propeller to remain stationary to the ground for the wheels to match the speed of the conveyor.
In this case, the plane would not take off, as the speed being measured was the speed of the wheels matching speed of the conveyor, not the airspeed vs speed of the conveyor. To sum it up, the plane would remain stationary to the ground and thus have zero airspeed (assuming no wind) and not be able to take off.