The zombie apocalypse MMO.
First order of business is deciding on the type of zombie. Going with fast zombies -- such as Left 4 Dead's -- certainly has its draws. But by choosing the original reanimated zombie, the game could have vastly superior numbers of living dead mobs attacking players. As a bonus, the original zombie doesn't infect with a bite since a person has to die and then come back as a zombie. Granted, this being a game means even if someone were to die they'd just resurrect with some kind of insignificant death penalty anyway.
I vote for slow zombies. While just a few pose no threat, it's much different story when a few hundred come pouring into the fray. Plus it's much easier to balance a game when you don't have to factor in the movement speed of a running zombie.
Real-time combat is a must. No quasi turn-based mechanics allowed. Hell, it's not like the MMOFPS is an entirely new concept either. Headshots, flanking your enemy and all sorts of clever combat tactics should come into play. As for character progression, I think a skill system is best. No need for levels here, just simply use a weapon and get better with it. Each type of firearm, armor and gadget would have its own advancement tree.
most of us play MMOs with friends and family. Sure, you can meet online friends but they're always going to play second fiddle to your roommate, spouse, sister or best friend down the road. So the game world would exist purely through massive instanced content, while private party instances allow friends and guilds a place to slay zombies without bother.
That's not to say there wouldn't be massive survivor towns that everyone could defend from the occasional zombie swarm. But there'd also be instanced encounters where six or seven survivors have to run into a mall for precious goods, then escape while carrying their loot.
Then we come to PvP, which in a zombie apocalypse isn't actually that much of a challenge to rationalize. Some people will come together in order to better fight the huge undead numbers, yes. But there'll always be other factions that see things differently. Some may want to run a democracy and free trade just like the old days, while others may believe the zombies are a biblical sign and form a massive theocracy. Then you've got the biker gangs and raiders, who're only looking to take what they want and kill everyone who gets in their way.
The rest is just filling in the blanks, but on paper -- assuming you can get the tech to make it happen -- this game works amazingly well. Another big factor to why it works is that the world is still beautiful in some ways. The sun still rises, green grass grows and structures still stand. Players won't have to be constantly inundated with images of death and destruction as in a nuclear apocalyptic setting. Then, when everyone is ready, they can load up on skills and equipment and go out to shoot every shambling thing in sight.