For my money zombies in Dungeons & Dragons (and its various retroclones) have never captured the true feel of the undead we know and love from the films of George Romero or The Walking Dead.
Here is my humble effort to correct that...
#ENC: solo, 2d6, or 3d20 (herd).
AC: 8 
ATK: 1 grab (1d4), then 1 bite (1d8)
- Immunities: 100% resistant to sleep, charm and any mind-control magic.
- Spread The Love: When a zombie attacks, its first attack will be a grab (for 1d4 damage) and then once it has grabbed a victim the next round it may attempt a bite attack (for 1d8 damage). As long as it keeps hitting each round the zombie may continue to bite, however if it misses its attack roll its next attack must be a grab and it cannot bite again until it has scored a successful grab. If a bite attack causes its victim CON damage then the target of the attack must make an immediate Saving Throw (at -2) to avoid becoming infected with the 'zombie plague'.
- Zombie Plague: Someone inflicted with this disease - which can be cured by Cure Disease - loses one point of CON every half our until they are dead. Once dead, whether through CON loss from the plague or simply the normal course of combat, they will rise 1d10 minutes later as a mindless, flesh-eating zombie. Note: once the victim is dead it's too late to use the Cure Disease spell on them.
- Damage Resistance: The first time the player-characters encounter this type of zombie for every weapon hit they score the DM rolls a d12. Only a result of "1" does the attack actually do full damage, indicating a head blow. Otherwise the weapons just do a single point of damage (plus any magical bonus) per strike. A zombie can never be reduced to below 1HP this way, though. The only way to kill them is through destroying their brains. Once the player-characters realise these zombies can only be killed by a head shot they may target the head with a -4 penalty. Magical attacks, however, do normal damage.
- Slow: A zombie always attacks last in a combat round, unless it has won surprise over its victim.
The walking dead emit a low moaning sound most of the time and some scholars speculate this is a primitive form of communication.
Although the flesh-eaters rely in sight for close-range hunting, at longer ranges they are attracted by noise - so a party making a loud racket may well attract large crowds of zombies if they are in the region.