A realistic zombie invasion? Well, to be honest, Left 4 Dead and 28 Days Later have the zombie idea down better than most every other zombie thing out there... thing is, zombies couldn't be literally "walking corpses", they would be some kind of infection that decays parts of the brain causing the human to see any moving, living creature as it's prey, and remove the logic to plot out a strategical attack against it... causing the "zombie" to sprint at whatever the victim is, with no caution to consequence, and devour it.
What's the chance? Really, really low. A disease like that, completely unnatural (it's never happened before, has it?) would have had to be caused by humans... if scientists wanted to create a "zombie", they could sit in a lab for years with hundreds of human test subjects and eliminate key parts of the brain until the subject acts like a zombie from Left 4 Dead... but nobody has the time, the patience, or the freedom to do something like that. Plus, it has no benefit. If someone tried to create a cure and a "zombie" was the side effect... the cure/vaccination would be so intricate, it wouldn't be possible to create for hundreds of years.
So to be perfectly honest, a zombie apocalypse couldn't happen for... at least a long time. But, I hope you see, that it is completely possible.
Hey, email me sometime if you like talking about this kind of stuff... tell me what you'd do in a zombie apocalypse.