In the Resident Evil series, bats, crows, and insects all serve as major annoyances, especially considering the fact you often have to save the precious few ammo you have, and back tracking through the areas is required, so you often have to decide if you want to waste your ammo fighting weak but numerous enemies just to clear the area, or let them be and risk losing your equally precious health if one managed to catch up. It came to an extreme in Code Veronica when a certain part of the level that is well-traveled came complete with respawning moths that could also poison you, which made that area a nightmare in terms of healing.
The Nintendo DS port of Resident Evil employed these to horrific effect in the game's Rebirth mode. The mode allows for multiple enemy types in the same room, which usually just means the game tosses a single crow or dog in with a roomful of zombies. Doesn't sound so bad? Well, y'know how a single match can burn down a whole forest? Yeah, it's kind of like that.
Resident Evil 6 had Screamers, mutated zombies with with a deafening scream. They're not too tough, but have some very annoying qualities: their scream not only attracts other enemies but makes them more aggressive, they tend to run away once attacked (meaning you're being swarmed by extra aggressive zombies while trying to fight them), and their scream stuns your character long enough to be swarmed by said extra aggressive zombies. They're also quite difficult to take down from a distance because, unlike the other mutated zombies, they're hard to recognize until you (far too late) see the pulsing red lungs.
In Alone in the Dark (2008), Vampirez are bats that attack if the player gets too close and are almost impossible to hit. Since they look like bats and are minions of Lucifer, they could be literally considered to be Goddamned Bats.
Shibito Brains from Siren. In some stages where they're present, you need to defeat them to win. In others, it just helps a lot, as if they're knocked out, so are all other shibito on the stage — and these are generally composed primarily of theextremelynasty Crawlers. Where they enter Goddamned Bats territory is that they can detect your presence without actually seeing or hearing you, and their usual response to this is to suddenly run away. It's actually a comparatively good thing when you instead get the sort of Brains that respond to your presence by charging in and attacking you.
There are also the Inu Shibito. Despite having a somewhat weak attack and being relatively easy to kill, they're a lot faster than you, and more often than not attack alongside more powerful shibito, forcing you to attempt to separate the Inu from whatever it's following and probably getting hurt by it in the process. They're much harder to deal with if you're unarmed, since the only thing you can exploit is their lack of climbing and door-opening abilities.
The Ariels in Silent Hill: Origins will have you pulling your hair out. They're small, fast, difficult to avoid, tend to attack in groups, recover very quickly when knocked down, and have an obnoxious grab attack.
Dead Rising: Chop Till You Drop, the Wii port of the original Dead Rising, features zombie parrots and zombie poodles alongside regular zombies. The parrots fly around squawking and stalking you until you stand still long enough for them to divebomb you. The squawking is rather annoying. The poodles move quickly, are hard to hit, and will lunge at you and tear off a piece of Frank. Oh, and a few bosses from the original were removed as bosses, and are now featured as special zombies. Note that they seemed to use only the most annoying bosses that everyone hates. The fat policewoman? Now she's everywhere, and dual-wields tasers, and takes more bullets to take down than a regular zombie. The annoying photojournalist who you wanted to kill from day one? Now he's a running zombie that kung-fu kicks you in the face and throws Molotov cocktails. And no matter how many times you kill them, they will come back.
Cliff is also placed as a special zombie in this version. Yeah.
Alan Wake had Goddamn Crows/Ravens, which would have players scanning the skies to spot where the damn avians would come from during their attack segment. More all the more annoying when crossing the plank bridges, since you can easily fall to your death while trying to fend them off. In the first DLC "The Signal", there are Goddamn Books that acted like the Taken ravens.
The Fish-Imps in Rule of Rose. Their legs have been tied together, so they can only haplessly jump after you, and their main attack is to fall down and flop around helplessly. Sounds silly until you're in a narrow space with dozen of the creeps between you and your destination, and you realize that their attacks are omnidirectional and impossible to dodge.
Even the ordinary Imps can be an annoyance, as they tend to attack in large numbers, and grab on you, forcing you to shake the left analog stick vigorously to free yourself, only to be grabbed again from the other side.
Alien: Isolation, like every other Alien game, has the facehugger, which waits patiently until you are somewhere you least expect it to be, then pounces and ends you in half a heartbeat. It's hard enough to hit as is with any of your weapons- the revolver is too slow, the maintenance jack is melee-only, the shotgun makes too much noise and can alert the other, bigger brother that also kills in one hit, the railgun takes time to charge each shot and the flamethrower wastes too much fuel while being better suited to warding off the Xeno.
Fear Effect has the aqueduct workers in Fear Effect 2: Retro Helix. Despite never actually attacking the player unless provoked, they are incredibly annoying for several reasons, chief among them being that they raise Hana and Rain's fear meter, even though all of them are cowering at the very sight of Hana or Rain. Then, as if that wasn't enough, killing them leads to a very difficult late game boss fight, where Hana has to resort to melee combat against a guy who shoots electricity out of his hands. And finally, due to the automatic targeting system, it winds up being very easy to hit them by accident, forcing you to put them down as a result.