I think that zombies play second fiddle to the real horror of a zombie apocalypse. The real horror I speak of is a world without morality. Because zombies are mindless, they are more like forces of nature and just as there is no morality implicit in a hurricane or earthquake, there is no morality in the zombie's urge to destroy and consume.
The pathos in zombie films is generated by the moral struggle of the "living" characters (as opposed to the undead): how do you resolve killing creatures that were once your family, friends and neighbors?
I think Romero's films capture the horror, tension and dilemma of morality in a world where morality has, essentially, disappeared...
Zombie films also tend to be nilhistic, in that the survivors all know that eventually they will be killed or exiled by the millions and millions of undead.
Max Brooks' World War Z novel upended the bleak future that most zombie fiction paints by describing a world AFTER the zombie apocalypse. He also addressed the moral dilemma created in post zombie-apocalyptic world quite accurately.
In the end, I don't think zombies are quite as terrifying as the idea of what we would become in order to survive in a zombie infested world...
P.S. This Wikipedia article may be of some interest to zombie afficianados:
http://en.wikipedia.org/wiki/Uncanny_valley