I've been rattling this around in my head over the past month or so and I think the ideas have crystallized enough to write them down and ask the group about them.
A DM can be many things depending on the game, the players, and his/her own personality and strengths. But I think there are two basic archetypes: Feeder and Arbiter.
Feeder: This is the style I'm most used to. In fact I'd say that 90% or more of the DMing I've played under has been this style. The DM comes up with an adventure, makes up a fun plot and a bunch of details along the way, and then he sits the players down and works them through it. By carefully feeding information to the party he guides them from point A to B and so on until the party triumphantly wins the day and marries the princess, or whatever "winning" looks like. The DM has to do a LOT of prep work ahead of time in order to have his ducks in a row and not keep the players waiting as he mulls over every detail, and to be sure he has a well-flowing plot.
Arbiter: This is honestly an unknown style to me. I've seen snippets of this style mixed in with Feeder style, and I think it could work out, but I'm just not sure. Anyways, as the Arbiter, the DM plays referee for the players, and the players come up with the story as they go. So instead of the DM saying "you're going to rescue a princess from a dragon's castle," the players say "hey, wouldn't it be awesome to go an an epic journey to a castle where a dragon keeps a princess prisoner?" And you as DM say "ok, what are your first steps?" And then the players come up with the whole thing. The DM sits back, enjoys the story, throws a few monkey wrenches in there, roleplays (some? most?) of the NPC's, but isn't even averse to letting the PC's roleplay some of the NPCs themselves, plays the role of their adversaries both socially and in combat, and referees the players so that things don't get out of hand (i.e. "I see a dirty peasant. I kill him. Holy smokes he's got a vorpal longsword hidden in his jacket!"). The DM must have a pretty thorough understanding of the campaign world, and honestly so would the players, but the onus is on the players to come up with the story, motivations, etc., and the DM is there to referee, add details, throw monkeywrenches, and play the opposition.
Has anybody successfully used the Arbiter style? I love DMing but I hate all of the prep work. And I'm always bummed for my buddy when he DMs and players aren't too into his story. So I think that maybe just having the players drive the story from the get-go may be a better approach for me. But it's a mysterious unknown to me!