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").
Neverwinter Nights custom servers do exactly this! DMs are always there causing changes to the world based on what players do and organizing all the twists etc.
And on top of that, in the one I'm following at the moment, the world is being eaten by a void and the rumor is that when everything is gone that's gonna be the end forever
GW2's Living World had storylines that lasted for months with permanent changes to the world. Although there weren't really any or much changes during this few month period, only between those periods.
And, obviously, (3) how do you recoup a multi-year investment across the period of only some months? Making games is extremely expensive and MMOs are by far the most expensive type to make.
I guess you could restart the whole thing to let new players join or people replay it. I am envisioning something like Mass Effect or Skyrim, which made money, but with thousands of other people with you. Perhaps I am underestimating the cost of the servers.
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").