One of the innovations in the d20 rules that was made by the Paizo folks was the Combat Maneuver Bonus/Combat Maneuver Defense scores.
Basically they took all the fiddly 3E combat actions (disarm, trip, bull rush, grapple, etc.) and turned them into this formula:
CMB = BAB + Str + any special bonuses (in other words, a basic attack roll, modified by feats/class abilities).
CMD = 10 + BAB + Str + Dex + any special bonuses.
I'm considering using the basic formula for my Classic D&D games for whenever anyone wants to do something like swinging from chandeliers, flipping their cloak over the opponent's head, throwing sand in their eyes, or the above grapple/disarm/trip type stuff.
I'm already using ascending AC/attack bonus, so this would be easy enough to add in. For monsters, they just get normal attacks, and 10 + HD for CMD (maybe the creatures that get a Strength bonus/penalty to damage could factor that in as well).
Simple, easy, and hopefully will make for more dynamic combats than simply "roll to hit, roll damage, rinse and repeat."