Chose about once. Really hard to determine, it can vary so mch by the encounter. Generally, dumb monsters will provoke a lot more than smarter ones. I've had encounters with wads of zombies where I probably deliberately let them provoke 3-5 times in a single combat. Then I'll have a classed NPC that never provokes at all.
Intentionally. The PCs in 3E have plenty of ways to force AoOs on enemies. Tripping and the mechanics of reach alone account for a lot of them. Then some PCs might take Hold the Line, Robilar's Gambit, or what have you. So AoOs are moderately common, maybe on average 2-3 per encounter total, in my games. But for the ones caused solely by NPC choice, ~1 per encounter is the most accurate.