It's a moving target, at least for me. When we roll initiative depends on how much granularity we need, particularly when it comes to the players. Some of the unusual situations we've ha come up...
1. Move to intercept
NPC makes aggressive move toward another NPC of lesser social class who insults his lord, and a PC moved to intercept the attack. They didn't want to escalate to full scale violence (at least not yet), and I preferred the attacked NPC to finish what they were saying. Also when it comes to combats where the objective is to defend a single NPC with low hit points, I've found it's hard for the PCs to win. I let the PC automatically parry the attack. If combat had already begun, however, the PC would have needed to win initiative and ready an attack to attempt somethin similar.
2. Planning an ambush
When I know there are stealthy bad guys about, and the PCs are entering dangerous terrain on guard, I've had them all roll initiative at a false alarm (raven bursts from a tree), and then used that initiative later on when they were surprised. However, for the purposes of readying actions and such, the PC are acting within an initiative count. This created a considerable amount of tension and unease.
3. Chaotic and simultaneous combat
I ran a mass combat which focused on the PCs responding to a level number of varied opponents and fluid battlefield conditions. To spare myself headache I didn't track initiative and instead had everyone (monsters too) declare their actions and resolve them simultaneously, allowing for freer resolution of ready/delay/synchronize/respond to scenarios. It worked very well for mss combat but not sure if I'd use it for anything else.