Initiative

When I was still playing second edition AD&D, I disliked the rules for group initiative—I preferred to trust in my own luck—but now I see the utility of group initiative and appreciate its simplicity. When I run games, I tend to roll minor NPCs as a group anyway, and with the PCs rolling individually most initiative rolls tended to as much about what order the PCs go as anything else.

Group initiative does what it needs to do without any giving you any excess information, and it takes less time that going around to record each player's initiative. It also gives the PCs greater flexibility with their tactics. The PCs can act in any order they want, which prevents some common combat mishaps like getting caught in an allied spellcaster's area of effect spell.

In the past, I've run combats without any initiative rolls at all—sometimes out of design (combat tends to have a different feel when you slip into it rather than formally starting it with a call for initiative) and sometimes because it just slips my mind to roll for initiative. For a short time, I played with a group that went around the table during combats just like they were doing exploration turns (the game wasn't D&D but the game's structure was very much like exploration in D&D).

In some games initiative is such an ingrained part of the system that group initiative doesn't work without some major hacking. For example, third edition D&D characters have multiple traits that feed into their initiative bonus, which makes it a little unfair to some characters to take away that advantage without replacing it with something else.