Before I go into the reasons behind not using initiative order, I’d like to explain how you can go about not using it. For those who have played Dungeon World (or some other game that I don’t know of that doesn’t use initiative order) and already know how, you can skip down to the Why section.
Dungeon World uses a narrative initiative order (okay, so it’s still technically an initiative order, but it’s not an ordered order), which means that story dictates who is next. There are times when the story doesn’t have a strong opinion (or any opinion, sometimes) about who should go next, so you can use a couple other ways to pick out who is next. If someone hasn’t gone in quite a while, maybe you should try to get that person involved now. You could also go off of whether someone has given any indication of having an idea of what they want to do next. You could even cause a player who gets bored easily to go more often to keep his interest.
The first reason for not doing initiative order has to do with one of the first things involved with having an initiative order: writing it down. The GM has just described a scene, working hard to get you involved with what’s going on in the story. Then comes the initiative roll; rolling dice is fun, but there’s always a wait involved when trying to get everyone written down (or whatever you do) in order.
The next reason has to do with a problem that people are constantly trying to solve for games with initiative order: bored people. Some players get bored or distracted more quickly than others. With the ability to simply choose who goes next, you can get those players to have their turns a little more often, keeping them engaged. It generally doesn’t throw balance off that much, and it helps everyone stay tuned-in.
The obvious reason for using narrative order is that it flows with the story better, being “read” more like a novel.
Lastly, I have my personal favorite reason: cool stuff happens more. A lot of times, in D&D, I would come up with something fun and cool to do on my turn, but with everyone else taking their turns, my plan would end up worthless. With the freer turn order, you can give some sort of indication that you’d like to go next, and then the GM can choose you. That’s been one of my favorite things about playing Dungeon World.
Pitfall of Narrative Order
There are sadly some games that work very poorly with an unstructured turn order. Most of the D&D editions wouldn’t do so well due to how determining when certain conditions take effect and such. It wouldn’t be horrible to do it, but you’d be messing with the game’s balance a bit more than in other games
So… yeah, I highly recommend a more free-flowing turn order system like this. Check out Dungeon World for more info if you’d like.
You can use Narrative order for any game where the bad guys don’t need to do active turns. D&D, Pathfinder, and 13th Age can’t do it since the monsters need to take a turn, but systems that can do an entire exchange in one roll (DW, FATE) you can do it since then the monsters are still doing as much as the players.