Yes, we've run several campaigns that way.
The way we do it is pretty straightforward.
First, we (the players) decide on a map of the world. We've used Middle Earth, Forgotten Realms, some from Steve Jackson's site, even the real world. They all work.
Second, we decide on the long story goal, the grand mission that is going to take us all over the world in search of pieces, clues, whatever.
Finally, everyone picks a part of the world that they're in charge of. We don't have to use the entire map, and seldom come close, but each player picks a city or country that's going to be theirs to mess with.
Any house rules have to be agreed upon in advance, and any new sources for spells, items etc. that get suggested during play should also get group approval. After all, everybody is going to have to DM anything that gets allowed in.
Every player has a character who comes from their home territory. When the party is adventuring there, the DM's character goes into NPCdom. They either leave the game entirely, off handling family business or hiding from creditors or whatever, or they just become minimally available.
For example, in our current campaign my character comes from Greece. (A village near Thebes, to be specific.) I ran the first adventure, the one that set things in motion.
All the PC's were sent by a sponsor to visit the Olympic Games, which were held in Athens. There they were to meet and discuss a major problem with the world: A curse that fouled the sky with dark clouds, blocking direct sunlight, and apparently even interfering in the ability of the gods to aid or guide mortal men.
While there I ran the Olympics, and some not-so-behind the scenes politics. The party got caught up in them, and the game was rolling. We ended the adventure with a huge battle as a Roman Legion fought a Vandal horde of about the same size.
Everybody gets Exp, including my character, even though his participation had been minimal. Why? Because, ostensibly, my character had been handling other matters that earned him matching Exp. He even gets equal loot.
The clue we picked up from all of this lead us to Florence, Italy, which belonged to a different player. He became the DM, and his character got tied up in local issues and couldn't be with us most of the time. We followed the clues, got caught up in the foul schemes behind a doomsday cult and eventually shut them down.
Then our missing friend rejoined us as our path lead to Rome, where our companion Marcus, a Jovian cleric, got called to Temple duty and we didn't see him for days. (His player was now the DM).
The PC in NPC mode gets the same rewards as the rest of the group, though not necessarily an exact match, so that DMing isn't a punishment or penalty for the character.
You might set a level limit for the campaign in the beginning, or the group might decide at some point that the story should be coming to a head. Maybe you finally find the last piece of that artifact, succeed in uniting the Seven Kingdoms, or follow the last clue to the Big Bad behind all the troubles.
But the story should have a strong thread, a continuous purpose that links all the adventures together. Some might be false leads or dead ends, leading to adventures that end up having nothing to do with the long term goal. That's okay.
The over all rule is simple, though: I run Greece, not Rome, so I don't get to assassinate the Emperor in the eternal city, and he doesn't get to level the Parthenon. Any changes or developments that affect another DM's territory or plot lines should get cleared with that DM ahead of time.
Now the DM styles and general quality of moderation and story telling will vary, obviously. You learn to take the bad with the good. Power mongering is strongly frowned upon, since any rule rape you introduce and push as a player or DM can and will be matched by someone else, and the whole thing turns into an arms race.
Ugly.
The final rule is simple: After a particular adventure, the group can decide that it was so bad, so far out of line, that it just never happened. It was a collective nightmare, a bad dream, and nothing more. We've only had to do that one time, and the DM/Player who ran it was a bit offended, but he got the message: No Death Star, storm troopers, Jedi or protocol droids in a D&D game. They just don't work.