This thread is scary, some people really need to learn some physics before commenting.
Regardless of how fast the treadmill goes, the plane will take off. If the treadmill goes faster, the plane's speed will be UNCHANGED, the wheels will just spin faster.
That's it, nothing else to it.
Not entirely true. If the treadmill could exactly match the rotational speed of the wheels, regardless of how fast they spin, there is no possible way for the plane to move, assuming the wheels don't slip, or get torn from the undercarriage.
This is because all the thrust must be used to get the wheels moving relative to the treadmill, which is very easy if the treadmill only moves slowly, such as at the planes takeoff velocity, but is obviously impossible if the treadmill always matches the wheel speed, since the net forces will always balance in this case.
Even if the wheels are free wheeling, which they are, there is still a small lateral force on the rest of the plane, due to the friction between the wheel and the ground, this must be overcome before the plane can move. Again, easy on the ground or a slow treadmill, impossible on a speed matching treadmill.
Caveats: It is more than likely impossible to get a treadmill moving fast enough to do this, and i doubt that the wheels could spin fast enough before exploding. However, assuming everything is 'ideal', a treadmill can stop a plane from taking off.
Summary: Wheel rotational speed matching treadmill + caveats: plane can't take off (probably not possible in real life)
Regular treadmill at planes takeoff velocity: plane takes off.