While I won't say I dislike zombies (given that I actually do enjoy the thought of them and the fact that it's an apocalypse that seems like it could be more than just me dying because of nature in an event that takes place in a few seconds), I'm a bit tired of them.
You see there's a few problems with zombies
1. They're an enemy I know all to well. They're recognizable. I've killed them in games just as much as I've seen them die in films. They're not some unknown horror, but rather now the equivalent of a pissed off alligator. It's unsettling to see, yes, but I know what it will do and that is bite me. However, I don't fear alligators to the point that seeing one will keep me up at night, because I know what they are, what they can do, their motivations, and that they are mortals.
Worst of all, I can recognize them almost instantly when they show up. I'm getting tired of every single zombie apocalypse having to explain to the new survivor that these are zombies. Do zombie movies not exist in those places?
2. They're too separate from humans. Brainwashed minions that twitch their way towards you shouting random pieces of advice are much more unnerving because when the question of "What's wrong with him?!" comes up, you reply that he's crazy, a state of mind, while you identify the zombie as such, a creature now different from a human. Sure both enemies you want to find out why they attacked you, but the zombie you're wondering why he turned. Yes it can happen to you, but if it does then you're dead, rather than losing your mind and still living, effectively killing you and yet not at the same time. The only zombie like this in recent memory would be the Infected from L4D, who according to the Word of God, have a strain of rabies, meaning more than likely they're actually still conscious just delusional as hell. However, an average player will most likely write them off as a zombie and just gun them down without any fear since that makes them less terrifying.
3. They're only able to shock, not scare. Given that this is Yahtzee's column you should all know the difference. Like I mentioned above, the most a zombie can threaten you with is death, rather than a fate worse that such. Sure we've all been told that the person is still there somewhere inside, which is what is supposed to make it terrifying, but it doesn't, since we always see those who get turned treated as if they were dead. Also, remember that the zombie's methods of attacks are actually limited compared to most other enemies, and that the most common are those animals use. We get at most a jolt of fear that kicks in fight or flight, not makes us feel unnerved for some time afterwards.
Compare this to any enemy at all armed with something that isn't even a weapon: a chainsaw. That rev is an unnerving sound that we all know as lethal, and is probably more recognizable than a gunshot to some gamers, as it's a warning. When used as a weapon, it brings up uncomfortable thoughts about the death it brings, a rather gory one that seems incredibly painful. It also carries with it a sort of distrust we all have of any item that goes incredibly fast a moments notice, as if we were unfamiliar with it being able to do so.
The other thing is that with a zombie, you know how they are made. Corpse + whatever is bringing things to life = zombie. Because you know half the formula, and know what the second half does, it doesn't ever really work your nerves as you try to figure out what happened (exception to this is once again L4D with the special infected, where you'll try to figure out just how the disease managed to produce 5 sorts of monstrosities from normal people). Compare this to stuff like Silent Hill, where you have no idea what these monsters are or how they are made, Bioshock, where you know these are people who over indulged on ADAM, but you have no idea how much they took, how long it took to change, or even what the person was like before, or even Alan Wake, where you begin out not knowing what caused people to change, if they needed to be dead to do so, what the thing behind the scenes could do, or even what the process was to be Taken, and you'll see that zombies are just too simple in construction compared to other horror enemies.
4. There's a reason they want brains. Nothing they do seems to indicate intelligence, meaning you're fighting a dumb enemy. They charge forward into gunfire with no survival instinct, an action that further separates them from a thinking person. Since they do actually go down from this (unlike certain invincible enemies that hunt you down over the course of a game), it isn't that scary, and sort of makes them pathetic. Compare this to an enemy that just runs past you rather than at you, getting you unnerved because if the attack doesn't come immediately, you feel them plotting something. Or how about an enemy that isn't going for the kill immediately, but rather goes about turning off lights or happens to only attack a few times before disappearing? However the worst would be the ones hunting you, intelligently keeping track of you as you progress, waiting for the right time to catch you off guard. Zombies at best might bump into something that causes you trouble or just found you when they were stumbling about looking for food.
5. There have been way too many as of late. Mostly I'm just sick of this. It doesn't help that unlike stuff like space aliens, there's little variety in them. You want to use undead in horror genre with a classic feel? Fine. Use walking skeletons, because trust me, they're much better. No one will be able to tell immediately how the skeleton came to life or even if it was from a dead body or not, or how to kill them. Also, while they would be separate from a human, they don't have an easily defined group name, and they're in a different place on the Uncanny Valley).