[butkus]

I was discussing this same topic with some Bengals and Browns fans. They swore that the plane of the goal extends outside of the pylon, and that players don't necessarily have to keep the ball inside of the pylon when diving for a touchdown. They claimed that it was a legal touchdown as long as the player is inbounds when he leaves the ground. What I long believed was just the opposite. The plane only exists vertically and that the pylons are the last part of the field that is inbounds. Thus, the ball would have to be inside or touching the pylon.
I went to the library today, and looked the ruling up in the Official NFL Rulebook. It is as follows:

Section 2 TOUCHDOWN
Article 1
It is a touchdown:
(a) when a runner (3-38) advances from the field of play and the ball touches the opponent's goal line (plane);
or
(b) while inbounds any player catches or recovers a loose ball (3-2-3) on or behind the opponent's goal line.

Section 38 TOUCHDOWN
A touchdown is the situation in which any part of the ball, legally in possession of a player inbounds, is on, above, or behind the opponent's goal line (plane), provided it is not a touchback (11-2).

As far as the question of whether the pylons are inbounds, the Rulebook states:
The four intersections of goal lines must be marked at inside corners of the end zone and the goal line by pylons mounted on flexible shafts. Pylons must be placed at inside edges of white lines and should not touch the surface of the actual playing field itself.

There you have it. The plane is only vertical because the ball has to be on, above, or behind the goal line, and MUST be possessed by an offensive player who is INBOUNDS. The ball can, however, touch the pylon because the pylons are inbounds.

Mystery solved!