A cooperative story-based MMO. Everyone is a participant in a months-long story that evolves in real time on the server. This is not just a world-wide event in a regular MMO; the world is progressively and irreparably altered throughout the story. I envision that the server simply shuts down at the end of the story.

There are two hard parts to this: (1) how do you make the game balanced even as the number of players fluctuates by orders of magnitude, (2) how do you make the game fun even as the amount of time each player spends differs by orders of magnitude. You will probably want key plot twists to be announced in advance so that as few people miss them as possible ("we predict the enemy hoard will arrive at our base on Friday around 8:15 PM").