This is my favorite old-school initiative system that can be applied to virtually any set of D&D-like RPG combat systems.
Each side rolls a die, the highest side goes first.
What makes this different from simple group initiative is who gets to roll each round.
A player is selected to roll for each round. Any modifiers for the system used are applied to the roll. This player goes first this round each player to the left on the winning side acts as they will.
Sure this creates some odd effects now and again but it's no burden.
Next round the player sitting to the left of that player rolls unless the character is completely uninvolved in the fight.
Typically the first player to roll in each combat is the point man or player at the fore-front of the marching order or the players can choose to keep trading rolls unless the DM upsets the order for some reason.
The DM is free to choose who rolls first among the players in unusual situations.
The DM may roll once for all foes or break foes into a couple squads based on position,leadership, and mobility. Thus it's possible for some monsters to attack the PCs before and after they all take their turn in a given round.
Fighting goes quickly, everyone get to roll eventually and there is a little room for planning and forethought (placing quick agile fighters in front).