We've established that magic doesn't exist, and there's no known force that has the power to revive the dead, so the classic imagining of the walking dead can be ruled out right away (and don't start talking about Haitian zombies, because we all know those aren't the ones depicted in pop culture). What we're left with is the modern re-imagining of the zombie virus.
Rabies is very similar to the zombie virus: it is commonly spread through a bite or scratch, and symptoms include confusion, violent behavior, and insomnia. But here's the thing - there's no rabies apocalypse. Likewise, there would be no zombie apocalypse.
The current Ebola epidemic of 2014 is a great example of a disease that does a bad job of being deadly - hear me out. The situation is tragic, but the reason it has infected and killed so many people is due to political instability and lack of first world education and infrastructure in the most affected regions. Ebola is a disease that spreads through contact with bodily fluids - a terrible transmission method relative to something airborne. The zombie virus is even worse, because it necessitates a bite (or blood mixing).
Worse still, zombies show clear symptoms. There is no carrier stage during which a person displays no symptoms and can infect others. Proper quarantine procedures and the (unfortunate) termination of infected would see this situation resolved in short order in a first-world nation.
Anyone who has played Pandemic or Plague Inc. knows that the best way to create an apocalyptic superbug is to fly under the radar while maintaining high infectivity. The disease's incubation period should be long enough to ensure that by the time humanity realizes there's a new virus going around, it's already too late.
Further, what happens to zombies when winter rolls around? They lack any sense of self-preservation, so they would freeze in the cold and die, if they haven't already starved to death. Winter doesn't send a human body into hibernation - hypothermia eventually leads to organ failure. And guess which important organ zombies of all mythos need to survive?
While we're at it, we might as well debunk all monsters. We've established that creatures living in our universe must obey natural laws, so that rules out anything that relies on magic to explain its abilities or physiology. There are some pretty frightening creatures in our world, but they aren't the product of a mad scientist or the nightmarish imaginings of an eldritch abomination: they're the result of millions of years of evolution and natural selection.
When considering the feasibility of a monster, you must ask a number of question. What does this species feed on? How does it reproduce? What is its natural habitat? What are the specific adaptations that have enabled it to survive until now? Why have we not discovered this species before?
Roughly 20,000 new species are discovered annually, but most of these are either insects, which are so tiny and numerous that they're more difficult to find and classify, or marine life, found in a difficult environment to study. We are not regularly discovering new species of land creatures large enough to pose a threat to man - there simply isn't as much place for such species to hide, undetected, as the depth of the oceans.
If humanity hasn't noticed the species, that means that humanity hasn't been interacting significantly with the species over the course of evolution. The creature, then, would not be adapted to hunt humans and would not pose a significant threat to us. To wit, I mean that in the same way that I mean a great white shark does not pose a significant threat to us: as long as you don't deliberately put yourself in a dangerous situation, like horror movie teens are wont to do, you're pretty safe.
So there's your pedantic overanalysis of fiction for the week. Does it stop you from enjoying horror games and movies? No. Does it stop you from being afraid of ghosts in real life? I hope so.
You know what you should be afraid of? Pirates. Science can't debunk pirates.