For years I've run classic D&D combat like this:
1. Players declare intentions.
2. Each side rolls 1d6 initiative. Tie = simultaneous effects.
3. Initiative winners do movement, spells, and attacks in whatever order they choose.
4. Initiative losers do movement, spells, and attacks in whatever order they choose.
5. Morale checks and other bookkeeping, if needed.
I know there are tons of variations on this combat sequence, many of them more complex than this, and that's fine... I settled on this sequence for my own games because it's fast and easy and the heavy drama of the group initiative roll is really really fun.
Recently, though, I've been experimenting with making things even simpler by dropping the player declaration step. I've been trying this for two reasons:
1. I want to speed combat up even more. Sometimes I'll referee for adventure parties with 8-12 characters, including NPCs and hirelings. It can take a few minutes for the party to decide on what their strategy is going to be - who's acting first, who's going to attack, who's going to hide, etc. Then they have to tell me what they decide. THEN I have to remember it all when the players' turn comes up. Of course I can never remember what all 10 characters all want to do, so they all have to tell it me all over again... Often this all feels like a drag at a game moment that should be fast, threatening, and exciting.
2. The primary outcome of declaring actions it is to penalize players even more for losing an initiative roll. While declaration might add a tough "realism" to D&D combat, in essence all it does is prevent players from reacting wisely to their opponents' actions. I am a firm believer in awesoming up my players, so I don't see anything wrong with giving players some consolation for losing initiative.
Anyway, the last couple sessions of D&D and Gamma World that I've run without declarations have gone great. With big groups the difference is obvious - everything plays way smoother and faster. For me quick abstract combat is a major attraction of old school D&D, and things just got even better.