Rolling Initiative is often a very cumbersome thing in games, so I have a proposal to automate it. This may not be a great idea but its just to streamline something that has often bugged me in playing actual tabletop games - getting everyone to roll and then working out who has the highest and then doing the same for potentially a lot of minions and monsters takes up a lot of time. I run a lot of Call of Cthulhu and whilst I usually wing mass combat for 50 cultists with machetes, a game recently slowed to a crawl when we had to roll for 5 players, their NPC entourage and a dozen enemy soldiers. Now with this being what it is, that stress seems like it could be entirely eliminated with a little tweaking, so here are my thoughts:
For every token, have a value along the lines of "Initiative" and have a space for it to equal either a value (in something like Call of Cthulhu, where it requires simply a character's Dexterity, say 12) or dice type + value (like in DnD, where you might roll 1d20 and add their Dexterity bonus, say 1d20 +).
Then, when the Turn Counter comes up, it might default to Highest Goes First (which you could turn off for systems where lowest value goes first). An additional thing I might propose (in settings which require rolling every turn) is the option to automatically re-roll all the initiatives when the turn order returns to 0 (something like Cthulhutech calls for this and it slows combat down even further).
A final idea is a mechanic for multiple actions - say an option to click something in the turn counter that enables a character to appear one or more additional times in the turn counter, either something along the lines of "x extra turns" (where this and other characters may appear again below everyone else in turn order) or "gets to act x initiative later" (where a character may appear again in the list at 5 initiative points lower down).