Stand Still lets you stop somebody's movement when you make an attack of opportunity against them. If an adjacent opponent moves out of a square adjacent to you (without withdrawing or otherwise evading the AoO) and you use Stand Still, does a successful hit stop them in the adjacent square or in the next square?
In the adjacent square
I can't find any specific clarification for this conclusion, so I based it on the way basic attacks of opportunity work.
Attacks of opportunity use your normal range, therefore they have to consider the enemy to be in a square where you can target them normally, not the square they want to move to. This implies that the AoO is resolved before the remainder of the triggering move, therefore the rule that states they cannot move any further during their turn comes into effect before they leave your adjacent square.
This fits with my intuitive understanding of how the feat is supposed to work. After all, if they could move a bit further it wouldn't be very "still".