My idea, tentatively called Mythogenesis, is in some ways similar to Emily's idea Caravan Solitaire in that it would take place in a wiki or similar electronic environment, and is aimed at the Living in the Future, and Unlonely your Fun challenges. It is inspired by games like "How to Host a Dungeon", NationStates, and Urgent Evoke.
The initial structural idea I have for the game is that players create their own deities, the worlds they live in, and ultimately connect to other deities to create pantheons and legends involving them.
The structure of the game would be something roughly like How to Host a Dungeon, but the step-wise results could/should be put up on a wiki to share. Players could then have their religions/societies rub up against others and combine in different ways. This would, however, not be necessary, and the game could be played solo.
The challenge, structurally, is to make a series of meaningful stages that create a rich tapestry of myths at the end.