Zombies have been not only been literally taking over fictional cities and worlds since Romero's Night of the Living Dead, but have also metaphorically been taking over our culture. Why are they a huge part of today's culture? They span over everything from movies, to shows, to comics, to board games (I actually just backed Tiny Epic Zombies), and many more mediums.
From the horror perspective, I reckon people you may know or be related to trying to now aimlessly eat you - is a pretty scary concept. But vampires fall under that same realm yet they're not as big of a deal. I think the lack of any intelligence or conscience in zombies is typically the main differentiation. So maybe it's the idea of people reverting back to their more beastly, lizard-brained state; makes us gravitate toward the genre.
Now what about the apocalyptic aspect of it? You could say that the more general apocalypse genre has a strong correlation with the zombie genre, in its popularity over the years. What makes us gravitate toward this genre, I believe, is the simplicity of it. After some apocalyptic scenario, such as zombies taking over, your list of goals just shortened to: survive. There are no bills, taxes, office jobs, high school drama, etc. You just have to find food, water, shelter, and fight zombies.
Disclaimer: I'm no psychologist or anything, I just like speculating about this kind of stuff. What do you think it is, why are we STILL obsessed with zombies?