Can I use a Combat Maneuver in place of an AoO?

Question

Does this require a feat? If not, does itself provoke an AoO?

For example, my cleric is standing between some guards and the rogue picking a lock. One of the guards walks through the square next to mine. In place of my AoO, can I attempt to trip him?

Answer 1

Yes, you can, if the Combat Maneuver is made instead of a regular attack.

Look at the descriptions of Combat Maneuvers. Some of them state specific actions, such as Bull Rush, where it says:

You can make a bull rush as a standard action or as part of a charge, in place of the melee attack.

In this case, you can not substitute your AoO for them, as you don't actually get a Standard action (or any other action type). This is for the same reason that you can't cast a spell as an AoO.

Others, specifically Trip, Disarm and Sunder state:

You can attempt to trip your opponent in place of a melee attack.

(or equivalent phrasings). You can use these three as part of an AoO.

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Regarding provoking an AoO

Note that even if you attempt a combat maneuver during an AoO, you are not exempt from the usual rules of combat maneuvers provoking an AoO. You can prevent them by having the appropriate Improved ... feat (such as Improved Trip).

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Your example

1. Enemy leaves a square you are threatening (i.e. can melee attack into), thus provoking an AoO from you.
2. You attempt a trip combat maneuver as part of your AoO. This is handled exactly the same as if you did it on your own turn, including provoking an AoO and the potentially resulting penalty on your combat maneuver check (see Performing a Combat Maneuver)
3. Your enemy can continue his turn. If you successfully tripped him, the remainder of his move action is lost.

Answer 2

Short version: Yes you can and yes it provokes an AoO.

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Long Version: An attack of opportunity provides you with a single melee attack against the opponent who provoked the opportunity. As you can see from here, trip is a special unarmed melee touch attack. That means you can use it during an attack of opportunity.

You could also use any other special attack, as long as it is a melee attack. These include disarm and sunder. You couldn't substitute it for anything other than a melee attack, such as starting a grapple (although it say's it's like a melee attack, it's not a melee attack) and feint as both are standard actions.

As for provoking an attack of opportunity by performing a trip, yes you do. This is an unarmed attack and as such follows all the normal rules for them. The only way (that I am aware of) to avoid this is to have the Improved Unarmed Strike feat. This allows you to count as armed whilst performing unarmed attacks and avoid provoking attacks of opportunity.

So for your specific example the turn of events would be:

1. Enemy moves into your space, provoking AoO.
2. You declare trip attempt against the enemy as your AoO. This provokes an AoO.
3. Enemy takes an AoO against you for the trip attempt.
4. Assuming you are still standing and capable of attacking, you may attempt to trip the enemy.
5. Enemy completes the rest of their round.

Answer 3

Some maneuvers, including trip, yes. Others, like bull rush, no.

The key difference is that a trip may be used in place of any attack, while a bull rush requires a standard action.