"Zombies are the new Vampires" -
True Blood
Zombies are a great threat for lower level characters in any version of D&D. They can be deadly in groups, but are slow. They are affected by all the same magics other undead are, so Clerical turning or Radiant Powers really get to ..er...shine.
The trouble is that D&D-style zombies are stuck in in a old modality of just being undead shamblers. Think Shaggy from Scooby-Doo only more dead.
Zombies in the game
All Flesh Must Be Eaten by Eden Studios are much more deadly and their bite is lethal, just not right away. Plus there are all sorts of Zombies in AFMBE including what we now call "quick" or ""fast" zombies.
Of course the question has been and will be asked again, "why not just use Ghouls?". Well simply put Ghouls are eaters of the dead. If thought about I'd add subtle demonic influences to them as well to reflect the Ghoul/Ghul relationship.
Improved Zombies
Let's take a page from modern interpretations via AFMBE and define a few new zombies. Instead of full blown stat blocks, I'll just talk about how to make changes to your current game's Zombie. Let's assume a couple of basics. First, Zombies have no intelligence, they are slow, attack last in any round and had HD roughly equal to twice a normal human (so 2 HD in older games). XP awarded for these needs to recalulated up.
The Hungry Dead
This zombies appear to be most like Ghouls. Their stats are the same as a regular zombie but once they kill a victim they begin to eat it. They turn as if they were one slot higher ("Ghoul" for older games).
Plague Zombies
These might be the scariest of all. They do not appear to be any different than a regular Zombie until they bite a victim. Then the differences are more apparent. They look and act like The Hungry Dead, but their bite spreads the zombie infection. Anyone that is bitten (a roll of a Natural 20) becomes infected and will become a mindless zombie in 1d6 rounds. They can be healed by a cure disease, but once dead they are dead forever. These zombies typically have twice the HD as their counterparts.
The Fast Dead
These zombies also appear as normal, until the move. These are no shamblers, these zombies know the value of running. They have an effective Dexterity of 16 and can attack normally (not last).
Alchemical Zombie
Stats-wise this is the same as any other zombie. The difference lie in how the zombie was made. The alchemical zombie comes for a vat of foul smelling liquids produced by an alchemist and not a necromancer. These zombies can not be turned.
These types can also be combined, so a Fast Plauge Zombie or a Hungry Alchemical zombie is possible.