Here's a simple initiative system. Simple enough that someone else probably uses it -- but I haven't seen it yet, so I call dibs on the naming rights.
1) The GM rolls a die and the PCs collectively roll a die.
2) High number picks one individual from their side to act first. The action then alternates until everyone has gone. Ties go to the PCs, just because that's more fun for them.
3) But you know how pretty much all roleplayers have a complete set of polyhedrals?
4) Right. The GM and the PCs each have one set of polyhedrals to roll initiative with. Pick your die in secret, roll 'em simultaneously, they don't respawn until all 6 dice have been used once.
So initiative becomes a tactical metagamey thing. But a small enough one that it's entertaining instead of ponderous.