As a player, I love getting involved in the setting of a game. It's one of the things that got me hooked with Amber - character journals, trumps, campaign logs. It all added up to me developing my connection with the setting, and having some influence on how the world looked.
As a GM, I'm a world-builder. I put a lot of time into working out the details of the setting - the politics, the hidden secrets, the cosmic underpinnings, etc. Which is fun for me on its own, but in game, it's pointless unless I can get the players invested in the setting I've built.
I have an idea for a game (I'm thinking fantasy, but it doesn't have to be), with an eye towards getting the players engaged in the setting, and interested in the other PCs.
The plan is, have players come up with some general idea of what they want to play. Then we come up with some kind of order (picking numbers out of a hat, whatever).
The first player introduces thier character. Thier name, where they come from, what they do, why they're adventuring (or whatever). The player invents the answers to all of these from whole cloth, adding as much detail as they like. Name your nation of origin, talk about the government, economics, whatever. The PC does magic? What kind? That sort of thing. Enough to lay down a character concept, without stats at this stage. Depending on the player, this can result in a detailed chunk of world, or just a few broad strokes. Either way works.
The second player does the same thing. This time, though, the player can add on to the stuff the first player presented about the world - if the first player didn't mention their King, the second player can fill that in. The second player has to tie themselves into the first player's story in some way. A connection between the two of them has to be established. Maybe they're both hunting the same evil dragon, maybe they're both from the same village, or they're long-lost twins. Something stronger than both being in the same tavern, anyway.
This progresses through all the players. By the end, a real image of a setting should be starting to form. The last player benefits by having the widest range of thigns to plug into, but has to deal with having a lot more of the setting already defined. The first player doesn't have to try to figure out how their PC fits into the others', but they have to start from scratch. I think this ends up being sufficiently close to fair.
Someone (the GM, or a volunteer), needs to keep notes during all of this. If your group is inclined to use technology (as I am), this would be a great time to set up a wiki that all players can edit. Then the players can fill in thier story and setting details, and the world can grow and develop as the game moves. It also forces the group to assign names to things, which I find tends to deepen player involvement in the setting. The GM will contribute as well, obviously, and sneak in secrets and details of thier own.
My hope with something like this is that it will result in the players being more engaged in the world, in the plot, and in the interaction of PCs as something more than minatures on a battlemap.
I like to think that it could work both in a con game setting (take a long slot, spend the first hour or two on generating characters and setting, then go), and in a face to face campaign.
There are some clear flaws in this idea. The first is that it assumes that everyone wants to be engaged and involved in the setting and the plot. Some people game just to roll dice and kill monsters, and get annoyed when the other stuff gets in the way. This sort of game wouldn't work for them. On the other hand, it means giving up a lot of control for the GM. The GM has to let go of the idea of the setting as thier masterpiece, and embrace the idea of it being "our" world.