Truly anti-social levels of PvP would be a nice start. Murdering other people and taking their stuff should be the primary focus of the game. In fact, that should be the entire focus of the game. Their are other people. They have stuff. By the direct ordination of God, that stuff is fated to belong to you. It is your right, nay, your very duty, to brutally murder those people in a clever and unfair fashion and take their stuff. You must then taunt them in a fashion that is tasteful, yet mercilessly cruel.
Character Creation! If I want to play a morbidly obese woman with boils and a clubfoot and a tendency to mix stripes with plaid, so help me I shall! And thy shape shall reflect thy abilities, sort of like in GTA:SA, but without that disappearing neck thing that happened to CJ.
Combat, which will be entirely between players, will consist of locating other people, placing them between your balistically accurate, entirely unassisted ironsights, and pulling the trigger once. Maybe twice, if you're a crappy shot or you are fighting in close quarters. Several times if they have decent body armor. They will proceed to fall over, scream, bleed, thrash a bit, then die, leaving you to steal all of their shiny, shiny loots.
When you are not capping hapless passersby and taking their things, you shall be involved in incessant territorial conflict, as you and the clan which you are forced to join in the interest of safety in numbers fight to maintain a territory and a resource and production base. This base will consist of bunkers, castles, and similar large bullet and bomb resistant structures, which should bristle with guns.
Crafting will be carried out by robots, slaves, or people in fictional third party manufacturing firms. Resource gathering will consist more of taking territory (by force), sticking a flag in it, and holding on to it while AI peons do the mining than clicking a rock fifty thousand times. If you really feel the need to get your hands dirty, you can screw around with your guns, swapping trigger groups, barrels, sights, and whatever. Also, a complete simulation of vehicle engines, just for the hell of it.
No levels of any kind. If there is any abstract skill set for players, it will be based on in game actions and mostly revolve around stamina. And there will be lots of shiny toys like artillery that needs to have the maths worked out if it's to hit anything, so that you lot who can't shoot for anything in an FPS will have a way to even things out with the AWP whores of the world.
For no reason other than I think it is awesome, this hypothetical MMO must involve air combat between heavily armed helicopters, zeppelins, and the odd space station in L5.
There must be a huge bloody game world. Large parts of the game should consist of exploring this game world, finding useful stuff, securing it, and exploiting it before someone else kills you and takes it. Note that by exploring I mean driving around hell for leather in Mad Max jalopies bristling with guns and armor plating in a dystopian post-nuclear wasteland, looking for anything that might contain useful resources and isn't much more radioactive than the background.
Oh, and of course you'd need to have a detailed, fully integrated flower arranging sim, because I am a sucker for random moments of zen.