I chose "Every round", although that might be a bit of an exaggeration. Multiple times every session, certainly.
I can't agree entirely with your "Don't try to dart past active enemies" proviso, Quasqueton. One of the things that annoys me about AoOs is not the mechanics of it, but the fact that players (at least the ones I play with) seem to be so afraid of experiencing them. Everyone desperately tries to find ways to avoid incurring one. They're always five-foot-stepping or withdrawing or going the long way round to get from point A to point B, just to keep from being the target of an AoO.
To my mind, combat means you're probably going to get hurt. But you're also going to try to get it over with as fast as you can, and you're going to help your buddies out to achieve that goal. If that means I run right past an enemy and take an AoO, so be it, unless I know I'm in bad shape. And even then I might still do it if my character is desperate to help out someone else, or just too pumped full of adrenalin to realize he's dying. Just because I know how many HP he has doesn't mean he does. I've decided as a player that unless I'm playing my PC as a very cautious person, I'm going to stop worrying so much about either taking or getting subjected to attacks of opportunity. It makes the whole combat seem more fluid to me.