Yes.
There are only two questions you need to ask:
1) Is he in a threatened square?
2) Is he moving out a threatened square?
If the answer to both of those is, "Yes," then it provokes an AoO.
The properties of the square you are moving into are irrelevant (except in the case that it is difficult terrain, only insofar as it prevents you from making a 5 ft. step).
Note, also, that you still only provoke one AoO for one offending action per person. In this case, the action is moving, so even though you are leaving more than one square threatened by the same person, only 1 AoO comes up.
He has the opption of moving acrobatically.
In addition, you can move through a threatened square without provoking an attack of opportunity from an enemy by using Acrobatics. When moving in this way, you move at half speed. You can move at full speed by increasing the DC of the check by 10. You cannot use Acrobatics to move past foes if your speed is reduced due to carrying a medium or heavy load or wearing medium or heavy armor. If an ability allows you to move at full speed under such conditions, you can use Acrobatics to move past foes. You can use Acrobatics in this way while prone, but doing so requires a full-round action to move 5 feet, and the DC is increased by 5. If you attempt to move though an enemy's space and fail the check, you lose the move action and provoke an attack of opportunity.
The base DC for the attempt is the creatures CMD.
Note, also, that you still only provoke one AoO for one offending action per person. In this case, the action is moving, so even though you are leaving more than one square threatened by the same person, only 1 AoO comes up.
This is almost 100% correct but there is one thing I would like to clear up.
The only action that only suffers one AoO no mater how much it is done is moving out of a threatened square. If someone performs 3 unarmed strikes against a target, they provoke 3 different AoOs (assuming the target can perform them).
Note, also, that you still only provoke one AoO for one offending action per person. In this case, the action is moving, so even though you are leaving more than one square threatened by the same person, only 1 AoO comes up.This is almost 100% correct but there is one thing I would like to clear up.
The only action that only suffers one AoO no mater how much it is done is moving out of a threatened square. If someone performs 3 unarmed strikes against a target, they provoke 3 different AoOs (assuming the target can perform them).
I'd call that 3 actions, even if a full-attack is considered a single action. Each attack is discreet, a new thing the character is doing, as defined by additional rolls and such.
A move action, however, is defined (in this case) as moving up to your speed. Each square isn't broken up into its own action, so it's all considered a single action, whether you move 10 ft. or 50 ft.
Anyway, yes, there ARE actions that can (kind of) lead to multiple attacks of opportunity, but they are really made up of multiple smaller actions when you pull it apart. For example, casting a ranged touch attack spell while threatened will usually provoke 2 AoOs: one for casting a spell, and one for making a ranged attack.
I've seen players provoke movement AoOs on purpose just like this in the hope that the foe doesn't have Combat Reflexes. They are then safe to take whatever standard action they like with less risk of it being disrupted.
Or to take the AoO hit "for the team" and allow other party members to not be attacked when an AoO could apply
Of course, Combat Reflexes does screw with that at times