traditional "living dead" type zombies are impossible, but it's entirely possible these days to engineer a virus that would cause similar behavioral reactions. just look at the rabies virus, which if left untreated, can already act in such a way, causing unstoppable, mindless aggression in mammals. it wouldn't take much for some black-budget genetic lab to speed up it's incubation time and increase it's transmissibility, and then boom, you've got a zombie-esque situation on your hands.
So remember, when you're feeling very small and insecure,
How amazingly unlikely is your birth,
And pray that there's intelligent life somewhere up in space,
'Cause there's bugger-all down here on Earth.
Loki/Grendel/Gail/Beowulf/Camilla/River/Bathory/Arwen/Lafayette/Deb/Jack Skellington (soon)