Here's my take on the idea.
The zombies would be infected by an untested bio-weapon that had unimaginable consequences, plunging every major landmass into chaos.
The zombies would not be undead, however their body would endure a form of necrosis (some rotting flesh, open sores, etc.), and have a swelling of the brain, not unlike Mad Cow Disease, causing huge aggression and dulled intelligence. There would be a varying degree depending on the area (length of exposure or the areas which were originally attacked).
The infected would also include some forms of animals (only mammals, however), and would act in the slow-lumbering manner until disturbed, at which point they'd end up running, leaping and killing much like Left 4 Dead/28 Days Later/Day of the Dead.
They wouldn't have incredible strength for the most part, however due to nervous system suppression, they couldn't feel pain and could push their bodies further than humans (no lactic acid buildup etc.) They would consume human flesh, but not simply thirst for it-It would be a matter of survival. They also cannibalise their dead and attack infected that aren't of their species.
Various cities that you can choose to start in, each with different bonuses.
I.E:
City 1-Better starting weapon(s) due to abundance/military rule/whatever.
City 2-Safer buildings, due to less direct attack (the infection would be a runaway bio-weapon).
City 3-Much smaller, but a survival bonus due to longer infected period/hardy people.
Large, desolate areas between cities.
I.E:
Deserts, ruined suburbs, post-apocalyptic highways, forests, tundra and so on.
These would be instanced, having to pass through a checkpoint to leave the slightly safer cities.
Teams could go here to find salvage, do quests (rescue, search, attempt to find cure/ingredients for cure, extermination of known infected hotspot, which would be a random location each time).
Maddened people could be found, who were semi-hostile, however they attract horde attention if encountered.
Raider-esque people who prey on areas with less infected (the randomised "hotspot" areas would be avoided), both on the loot within ruins or abandoned vehicles/barricades/hideouts, or the survivors who venture out of the cities.
PvPvE:
PvP servers would take a different aspect, where you play as an instantly-maxed out human who has recently been infected, driving them mad and increasing their abilities somewhat, though they still retain cognitive thought, at least enough to pick sides and use weapons.
Additionally, during PvE, the normally moderately safe cities would encounter a full-on zombie attack, which would cause rioting. Survivors versus rioters versus AI zombies.
These attacks would change whether a city was abandoned or kept safe, depending on the outcome. Other settlements could join in and help, or if the city is lost, it could be reclaimed a few days (only hours in real world time) after infection, if you manage to drive them back.
Weapons and armour/equipment:
Would generally be salvaged, and in typical MMORPG fashion, rarity is a factor. The rarest and best weapons would be pre-infection weapons found in heavily infected or pillaged bunkers and fortifications, and best armour being found in a similar vein. Plenty of different non-weapon/armour equipment is available, too.
Classes:
In PvE, all players start out as the same, survivor humans. As you level, you choose traits, knowledge paths and training.
I.E:
Trapper (leans towards making traps, discovering traps/danger areas, gains more salvage than other classes, and uses light weaponry, such as melee weapons and handguns. Downside is the lack of armour and heavier weaponry).
Seeker (focusses on assault weapons such as machine guns, SMGs and shotguns. Can use medium-size weaponry and excels in close-combat. Medium armour possibilities, and has the bonus of being far more adept in enclosed areas such as tunnels or corridors of bunkers).
Sentinel (primarily uses rifles and assault rifles. Has medium armour, and can use salvage to upgrade rifles with scopes. More accurate than other classes, but also has low salvage efficiency (due to needing specialist parts) and cannot deal with masses of enemies at once).
Greaser (has the most use for salvage. Can repair abandoned vehicles, fix weapons, fix defences and patch up armour of team mates, along with plenty more. Uses melee and short-range weapons such as SMGs. Has little armour himself, and not particularly agile).
Saviour (generally acts as a healer, providing medical help and psychological boosts to the team. While each "class" is able to revive fallen allies to a degree, only the Saviour can heal others while they are up, and permanently revive them when down. Can't use armour, and only carries a sidearm (pistol, micro-SMG).
Berserker (able to use the heaviest armours, these ex-soldier/mercenary/SWAT members have the best battle training, however this MMO would focus more on survival than head-on battles. The Berserker would focus on suppressing fire, attempting to mow down and slow the hordes, if they are encountered. Excels at taking Raiders out, and is able to use Light Machine Guns, grenade launchers and such. The downside is that they are the easiest targets, as they are cumbersome thanks to the armour and weapons. Also acts as a mule for the team, with the room and strength to bring some extra ammo, medkits or salvage).
Medkits would function as a real first aid kit would function-A small case filled with a variety of different things, which would be used by the player on themselves, or by the Saviour on anyone, for various afflictions.
I.E:
Cuts, gashes or bleeding wounds would require gauze.
Infection (not the zombie kind), or poison would require an injection of antibiotics or something of that manner.
Concussion, severe body trauma or broken/fractured bones would require a painkiller and further treatment.
Zombie infection would be possible if severely injured and bitten by a zombie, and it would require termination of the infected player by the party (it would not be permanent, that player would simply rezone to the city they left from).
The medkits would only have a certain amount of the aforementioned items, such as 2 rolls of gauze (2 uses per roll), 1 antibiotic/antidote syringe, 1 painkiller syringe (full recovery) and a bottle of painkiller tablets (5 uses per bottle, temporary recovery). Each player could carry 1 medkit, and only use it on themselves. They could however hand it to the Saviour, who could use it on anyone. The Berserker is able to mule up to 2 medikits in addition to his/her own one.
Wow, I got carried away.