Depends on what you call a zombie.
"Undead" zombie a la early Romero films can't exist. The moment you die, your body activity naturally stops. And unless you're revived very soon, your organs - especially your brain - dies from lack of oxygen. Your blood, without your heart to drive it, coagulates in your veins, making it kinda unable to carry oxygen. Your body goes "stiff". So, uh, without any source of oxygen, one's muscles wouldn't function. And even if the could, stiff limbs wouldn't really allow for a really menacing zombies. Yes, yes, I know, that's the main excuse for shambling for zombies. But really, imagine anything effectively walking or shambling on practically straight limbs without all the precision control your muscles allow you now. It would be pretty damn unlikely.
And the whole "attack people and eat brains" thing isn't really applicable here, too. With no digestive system, what's the point? And even if there was one somehow miraculously working, why would it require something this specific, especially given zombies' lack of reasonable movement.
Rabies-infested not really zombie a la 28 days later is somewhat more realistic. Rabies, as it is in it's current form in animals, does pretty fucked up shit. Pumped up aggressiveness, good chance to spread the disease through bite, fucks with your head - I'm pretty sure at later stages of rabies one suffering from it becomes hydrophobic, although my source might be outdated.
But that doesn't really allow for the "braaaains" type of zombies.
I could see some kind of sci-fi zombies a la bodies controlled by generic "nanobots" or devices, but it kinda blurs the line between cyborgs a bit. Or animated monstrosity, but then again a corpse that is able to move and do stuff because there's a robot underneath the rotting flesh is not really a zombie, it's more of a simple robot. Even first terminator did funny stuff like that, wrapping himself in human flesh to fail to avoid falling into a really dumb plot hole with the time machine.
Hmm, what else.
Voodoo zombies, those are pretty realistic. But then again, they are kinda what started the whole zombie thing. Although probably a good portion of lore comes from more ancient beliefs, undead aren't exactly rare in folklore. In my native Russia, there's a fucking evil skeleton wizard character that probably dates to before Christianity. While it's hardly a zombie, it's an undead, and given the fascination people always had with death it's very reasonable to assume that current zombies in some way inherited some things from older western undead creatures in folklore. But then again, I'm not too familiar with folklore aside from the really mainstream stuff like Kalevala and Illiade/Odyssey and a number of other Norse and Greek myths.
Pointless rant, back to voodoo zombies. A voodoo zombies is just someone forcibly drugged with a lot of crap, and led to believe they're dead and a zombie in service of whoever chose to do this to them. It's not that different from, you know, persuading a really drunk guy to do something outlandishly stupid, but more permanent and with more debilitating side effects.
And of course, in case of the voodoo zombie, the zombie is just someone REALLY stoned out of their mind, and I doubt that it's the pleasant kind of "stoned". It's not that far from techniques various cults use to improve loyalty, you make various rituals and stuff to stop your recruits from having enough sleep, maybe encourage some group ritualized drug consumption, anything to lower the focus of the recruits. And then you push your bullshit on them and they don't disagree too much.
Voodoo zombie is just like that, but with a lot more drugs and bullshit. And on a much smaller scale.