AoOs seem to show up about every other combat for us; ultimately, we try to follow the rules, but find them terribly annoying.
Part of the problem for us is trying to figure out what, exactly, D&D combat is trying to map. Actually this is true for most rpgs, but I'll limit the discussion of the moment to D20.
On the one hand you have fairly "realistic" feeling combat maneuver elements, such as firing missiles into melee, attacks of opportunity, and flanking (though this is handled terribly in the opinion of our group); conversely the entire combat is run from a God's Eye approach where the entire combat area is shown to the entire group, no chance of confusion over whether one is attacking friend or enemy or other "fog of war" elements.
In other words AoOs add to the "realism" of combat, but the battle board removes the "realism" at the same time. If you try to enter/leave a threatened area you place yourself in more danger, but it is very easy to calculate exactly where you need to be to avoid such matters and the whole 5' Step element reduces matters to a very schematic view of combat.
In many ways I feel that the only way combat would be logical and realistic would be to have all players hooked up to Virtual Reality machines, with the GM programming the assailants (but not actually playing them). That would lead to a "realisitic" feel.
Barring this, having no map board, no AoOs, etc., would map the more generally heroic, over-the-top approach of most novels, anime, movies, and the like -- description becomes everything.
So, yes, we incorporate AoOs, but only when they are unavoidable; when we have the right mix of players, we ignore them entirely, as well as many of the minutiae points of D20 combat, going for something more streamlined, schematic, and cinematic (less "realistic", more "fantastical"). That tends to suit our group better.