I forget what game it was from, but a couple years back I remember going over some rules for a game system I ran very briefly (I believe just one session) which had initiative set up in a neat way that I always liked.
The game had a cyclical order of combat much like D&D however the person with the highest "initiative" (it was called something else like perception or whatever. Can't remember it...) actually went LAST. In addition, the players would announce what their character was doing only but the action did not occur until after everyone had a chance to announce their action. Then you would resolve the actions either simultaneously or in reverse order (highest ot lowest), I can't recall.
So what that means is that the player with the lowest initiative would announce their move/action "Jorzan is going to run here.. blah blah" and the second lowest initiative and so on up the line. The benefit granted to the characters with a high initiative the ability of knowing what their targets were doing so they could react accordingly.
Taking this to a D&D example, an Orc with the higher initiative standing next to a wizard. The player of the wizard would actually state his/her actions first, even though the orc is technically 'faster'. So, going with the example from earlier in the thread, "Jorzan the Wizard moves 5' back and begins to prepare a burning hand spell at the orc!". But not actually role dice or do it yet.
Then the Orc (DM playing as the orc) would announce their move with full knowledge of what Jorzan has done and announce perhaps, "Seeing the wizard back away, the orc follows, axe overhead and strikes at the wizard and his hex!"
Then you would resolve them moving together (i sort of remember movement actions were resolved sort of simultaneously while other actions were resolved highest to lowest) and then the orcs swing would happen first, and then if that attack from the orc didn't kill or stop the wizard from casting the spell, the spell would then go off.
Well then. That was sort of a wordy description and not was not as slow and clunky to play as it reads... I thought it was a pretty neat system.