I recently read "Initiative: the Silent Killer" on Ars Ludi (no, I didn't get the idea for a D&D blog with a Latin name containing the word for "game" from Ars Ludi - I don't recall even hearing about it until after starting this blog).
The idea is that if you have the players all acting one at a time, they'll lapse into just waiting for their turn to come up, which means they'll stop paying attention to the game. Which, yes, does tend to happen.
So for the third episode of my Open Game Table, I instituted the suggested new rule: all the PCs go at once, and all the monsters go at once.
Whenever combat came up, I called for each character to roll initiative, confer amongst themselves, then tell me the highest roll. Meanwhile, behind the screen, I rolled initiative once for each of the monsters, and took their highest roll. Whichever group gets the highest initiative roll goes first.
Under normal rules, I would just roll once for each group of monsters, but if the PCs get to roll 6 times and take the best, and the monsters only get to roll once, the PCs will nearly always wind up going first.
Of course, this reduces the impact of things like the Unreactive flaw and the Improved Initiative feat. All you really need is one or two players with Improved Initiative, and everybody else can take Unreactive, and the PC party will still usually wind up going first. So an alternate method would be to have all the PCs roll, and announce the highest and lowest roll they made, which are then averaged together and compared to the highest and lowest roll of the monsters.
But if you're going to get that complicated, you could just average together all the rolls from each group and compare the averages. It all winds up unnecessary, and defeating part of what turns out to be the real reason to do it in the first place.
To wit: in practice, this method had negligible impact on how much the players were paying attention. (I think the players actually were paying attention slightly more than usual, but I think that was a combination of fewer people wandering in being distracting than usual and that I mentioned at the beginning of the session, as the justification for this experiment, wanting people to pay more attention, so they were simply more aware than usual that it bothers the DM when his players get distracted.)
Moreover, the "taking turns" mindset is so ingrained into players at this point that they still wound up effectively taking turns. Several of the most self-motivated players would take their actions, then I would figure out who hadn't yet gone and prompt them to go. This is not, however, bad - I was afraid it would be much more chaotic, but with this mindset still in place, it winds up being quite orderly.
The real benefit I noticed at the time is how much faster this method is at resolving initiative. Under normal circumstances, the DM needs to roll each group of NPCs, then take a number from each player, then sort all the numbers in order, then combat may commence. Unless the DM is really fast (I am not), he is the bottleneck on this procedure. I've played in games where one of the players is delegated to gathering all the initiative numbers and resolving an initiative order from them, which is slightly better, but still involves a bottleneck.
Under this system, the DM can roll all his NPCs and come up with one number while the players are all rolling and consulting amongst themselves, and once they come up with another number, they're compared against each other and instantly you know which team goes first.
I think in the event of a surprise round, I may forgo calling for initiative at all. I may even forgo the surprise round (where the ambushers get a half turn before real initiative begins) and say that the benefit of having a surprise round is simply that your group automatically wins initiative.
But perhaps the best part is that, under this system, none of the players has the opportunity to be a bottleneck on combat. Under a normal initiative scheme, there's always at least one player where you get to his turn and only then does he start thinking about what he's going to do, slowing down the pace of combat and making everybody else wait interminably. Under a normal initiative scheme, one must either tolerate this or resort to bringing in an egg timer and saying "you have thirty seconds to declare your actions or you forfeit your turn". Under this group initiative system, if you don't know what you're doing, that's okay, the rest of the party can go before you.