A medium-sized creature occupies one square when it stands. But what about when it's lying on the floor?
We had a troll with a reach of two squares that had just beaten my paladin (who was directly next to it). One of the other players said that since I was now lying on the floor, my PC occupies two squares and he can easily pull me away from the troll without granting an opportunity attack to the troll.
Is there any support for this in the manual?
No. The creature always occupies the same amount of squares, no matter the position.
Note that one square is not just where the person stands, it's the maneuvering area in which it might fight without any encumbrance from other squares.
Also, per KRyans comment, if anything, a creature lying down (not maneuvering and defending his space) takes up less room, not more. Which is why you can move through squares that contain downed hostiles.
Furthermore, as SSD noted, to grab and drag a prone ally you have to enter their square anyway, not just stand beside them. So even if a prone medium-sized creature did take up two squares, the ally would still have to step inside the reach of the troll.
Prone is not defenseless, so the creature takes up the same amount of space. A creature's space is its personal space, regardless of facing.
