Wow, I can see why this thread has gotten so long!
And, it's all the fault of the OP who thought he was wording his post cleverly enough to remove any ambiguities.
1. Those who say the plane can't move forward are, in a sense, correct. For if the plane was to move forward, we'd have a paradox. The conveyor *cannot match the speed* of the wheels on a forward moving plane, unless the wheels are skidding. People keep pointing to "if the plane is going 100mph, then the conveyor will be going 100mph in the opposite direction and the wheels will simply be spinning at 200mph." No, the OP said the conveyor matches the speed of the wheels, not the speed of the plane. 100mph doesn't equal 200mph, except in those trick proofs that require division by zero.
In other words, the speed of the wheels = the speed of the conveyor + the speed of the plane. Since conveyor speed = wheel speed, then logically, plane speed = 0. Anyone using that sentence as the basis of claiming the plane doesn't move is correct. You can't ignore this important fact. But, unfortunately, most of the people who have come to this realization don't quite realize the meaning of it. It's not a matter of the conveyor keeping the plane in place... it results from an impossible constraints on the problem.
2. If the conveyor matched the speed of the plane, rather than the speed of the wheels (which is impossible), then the plane would indeed take off, with the speed of the wheels always double the speed of the airplane as it accelerated down the runway. (assuming no slippage of the wheels)
--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
Now, for those who are saying that a spinning conveyor can keep a jet from moving forward (I've already established that the constraints given by the OP are impossible), try this at home:
Turn on a treadmill... set its speed to 10mph, but keep it level. Put on a pair of rollerblades. Skate across the room at 6 or 7 mph. Hop onto the treadmill while moving forward. Note that the treadmill does *NOT* stop you from moving forward, even though it's moving in the opposite direction at a speed greater than you're moving forward.