I'd say <10% of combats. Occasionally I will allow my character to intentionally provoke AoOs in order to get to another point in the location so my character can, for example, aid another character or attack a different opponent. If I'm playing the fighter and I end up facing off a bunch of low-level mooks that the other PCs can easily finish off while the boss monster is attacking the wizard, I'm going to go over there and attack the boss monster, even if that provokes an AoO from 5 mooks on the way, as long as my character isn't too badly hurt already to risk it.
I get the impression that a lot of players are terrified of AoOs and avoid provoking them at all cost. I don't understand this attitude.
I also get the impression that a lot of players and GMs think you have to make an AoO whenever circumstances allow. I don't understand this attitude, either. If your character is already in combat with someone else and another character runs by, why would the first character take his attention away from his current opponent to make a strike at the passing character? Sure, if the first character is fighting someone who's badly hurt or he knows isn't much of a threat, then it makes sense for him to attack the passerby. But if he's engaged in a life-or-death struggle with someone at or better than his own combat skill level, then maybe he'd better just keep his eyes on his current opponent.
I think turn-based combat tends to make you forget that combat rounds are only 6 seconds long and most of this stuff is actually happening almost simultaneously.