A friend of mine explained what he called Chaos Combat to me. Over time my own additions have resulted in the following. I've used this for 2nd and 3rd edition, so there will probably have to be some modifications for 4th.
- We play on a large whiteboard flat on a table. That way everyone knows where everyone is at and it is easy to draw the battlefield and make notes.
- There is one roll for monster initiative even when there are different types of monsters. All players roll initiative.
- I roll monster initiative and announce to everyone, "Before <whatever number>, go!"
- While they are going, if I think a monster will make it to the next round, I'm already rolling their to hit, who they are going to hit and damage.
- Players will ask me AC of monsters and roll their own to hit and damage and write the damage on the whiteboard next to the monster. If I notice that the monster damage is over a certain amount I lay the figurine down. (Don't worry, the players will remind you)
- Players can stack their initiative if they want, but after a certain amount of time if they aren't done, they lose their turn. If I catch them cheating their initiative rolls, The hit points of their monsters go up, or I auto hit them next round, no muss, no fuss.
- Magic and area effect is all handled by the players except for saves and damage.
- After a certain amount of time (usually by the time I don't have anything else to do or keep track of I move all of the monsters, remove dead monsters and then start announcing which players got how much damage. In a pinch I might point to a player and tell them to roll their own damage (fun to watch sometimes).
- I then announce "After <whatever number> in the first round and before <whatever number> in the second round, go!"
- repeat the process (keeping the same initiative rolls)
Probably leaving a few things out, but that is it in a nut shell. Yes, you have to trust the players as you as pushing a lot of the bookkeeping to them.
Rounds can take as little as 30 seconds. Even with 10 players at the table and tens of monsters I can keep all of the players almost constantly moving. (most players will be standing up around the table). The best battle I've had like this was 8 players around 7th level against waves of Orcs (about 20 at a time, numbering 250). We finished in 15 minutes and even the non-smokers had to go out for a smoke after that.
To me this is a more accurate system of battle as a well-tuned group can avoid most mistakes, but a disorganized group ends up walking into their own spells, doing extra damage to an already dead monster, etc.
Sure you lose some individual fun cutting all of the corners, but the group fun goes WAY up, and I've never had a serious complaint due to everyone really having fun with it.
Warning, if you play like this and go back to the normal initiative based system, you'll want to claw your own eyes out in boredom.