[SnowTroll]

Primarily mushes, though I've played a couple of muds where, if not outright required, turn taking is strongly encouraged, i.e., "Hey, you skipped me! It was my turn to post next!" It's not that incompatible of a concept with muds as people seem to think it is. People already take turns in roleplaying muds when you say or emote something, then wait for the other guy to respond before you say something else. In crowded rooms in a mud, it's just polite to let some other people do things between your actions rather than trample all over the scene, and in a couple of muds I tried in the past (that may or may not be "RPIs," but the primary gameplay revolved around speaking and acting in front of other players rather than traditional advancement mechanics), I've seen players deliberately organize a room into "round-robin" pose order once people started arriving. I've seen looser muds where turn taking is preferred, but with the understanding that a room can often include several ongoing small groups and conversations, and people in those small groups can have their own turn order with each other, independent of what's going on in the larger room as a whole.

I guess the bigger question/distinction would be whether there are (m)any muds where turn order is outright required by rules, which I imagine would be a rare thing. Every mud is going to inherently have a bias toward some type of turn taking, but it's normally too much of a pain in the butt to keep track of who's turn it is to roleplay and ask players to sit on their hands if they have something to contribute.