Zombies have a range of characteristics (to me). They are us but not us - they fall into the uncanny valley of uncomfortable resemblance. They are us but diseased, which triggers our revulsion instinct. They are our fear of death. They are the apocalypse, because the world is now ending and we cannot rely on civilisation to support us any more and must learn to survive on our wits alone. They are unstoppable - there are always more dead people than the living, and everyone who dies becomes one of Them. They are the fear of strangers, who might act in awful ways. They are the fear of madness - of people who look like us, but act in dangerous, unpredictable ways.
Having awoken from a nightmare and then laid next to Julie for a few seconds, not sure that she wasn't a zombie, waiting to hear her breathe so I could be sure she was alive, I acn sympathise with a lot of this stuff.
On top of that, there are things like The Infected from 28 days later - who tap right into my fear of people being angry at me. And things like The Crossed from the Garth Ennis comic, who come from his nightmare** that just under the surface of an ordinary person there lies a murderous, cannibalistic rapist psychopath who just wants to do awful things to each you.
As to the wider question of why paranormal stuff is popular - I think that paranormal ideas are largely about the facets of humanity that we find fascinating. Vampires are the dangerous killer in the night, and their seductive power. Succubi are people who are all about sex. Werewolves are the animal within us. Telling stories about them allows us to talk about the things that we find fascinating about ourselves, and manifest the ideas/drives into physical form. This is easier nowadays with CGI than it was thirty years ago, and that might be enough reason to make them more popular. And it's much easier nowadays to make a low-budget TV show and get it out to a tiny niche that's spread across the planet. So what was supernatural books/comics a decade or two back is now TV, because that's now affordable. I don't know why paranormal romance came back into fashion - any theories?
*The commas in there look completely messed up to me. How should I have phrased that?
**Literally. He woke up from a dream where suddenly everyone in the room turned, looked at him, and smiled, and he knew bad things were about to happen. And thankfully then woke up.
Original post on Dreamwidth - there are comments there.