There are a couple of D&D combat-related things I've read on message boards and blogs lately that intrigued me.
First, somebody pointed out an obscure rule buried deep in one of the manuals (the DMG? I don't recall exactly) that suggested that in a multiple-opponent melee, the actual enemy attacked should be selected randomly from all those within reach. The rationale, as I recall, was that the one-minute combat round encompassed and abstracted a great deal of maneouvre, feints, parries and blows, and that the nature of hand-to-hand combat is such that it is seldom possible to concentrate on a single opponent and that attacks are made whenever an opportunity arises as the combat moves to and fro.
I've never (consciously) read this rule, and I don't know if it is meant to apply to PCs as well as NPCs and monsters, but it does seem to me that it suits an abstract combat system. It would make it harder to work systematically through a group of opponents, since one couldn't be sure that one's attacks would be directed against a foe one had already damaged. If fighting alongside comrades, the party wouldn't be able to reliably spread their attacks among the available targets.
What I like about it is that it would make combat less mechanical and predictable. What I don't like about it is that it removes a degree of tactical control, which is not neccessarily to everyone's taste. I find the idea intriguing from a game-mechanics perspective, but I don't know that it would actually make playing more fun — and that's really the aim of the game, after all.
I think, if I were to adopt this style of play at all, I'd probably tend to use it in a miniatureless combat situation, and I'd modify it somewhat so that a character could concentrate on a specific foe at the cost of an AC penalty against any others.
Another thing that interested me recently is the idea of doing away with the attack roll, as proposed by JB on his B/X Blackrazor blog as a means to radically speed up combat. It's an idea that seems to me to fall into the same camp, conceptually, with my ideas about doing away with the initiative roll.
He points out that when a magic-user casts a spell at somebody, there is generally no to-hit roll required and the victim (usually) gets to modify the effect with a saving throw. He suggests that a similar sort of thing be applied to physical combat — I'm over-simplifying enormously here; it would be a good idea to go and read his actual words (there are a couple of other of his posts that expand on the idea; the one I've linked to is the first of the series).
Again, this is an idea that I think suits a highly abstract combat system, but I don't think it's an idea that many players would find all that attractive, for one main reason: people just love rolling dice. They may complain that playing out combat takes too much time (though in truth that's a problem I've encountered more in other systems, not so much in D&D) but when it comes down to it, they like the suspense of rolling a die and seeing whether they succeed or fail.