Goddamned Bats / Massively Multiplayer Online Role-Playing Game
In Final Fantasy XI, there are quite a few enemies that could classify as these. Ironically, the actual bats of the game are relatively tame and even make decent EXP targets for groups with piercing damage. As for Goddamned Bats, Tigers and Raptors are, strangely, very good examples. These enemies can detect you from a mile away, move really fast and can paralyze your entire party. They are rarely, if ever, used as EXP mobs and drop virtually nothing of value. Since the advent of the level cap increase, these monsters continue to agro players en masse, making them a huge pain in the ass when travelling through an older zone.
Honorable mention goes to Imps, which can detect you even when you're invisible. Though not much of a threat, they're rarely clustered together, making Tigers and Raptors that much more obnoxious to deal with.
The Devouring Earth Swarms in City of Heroes. Not actually that hard to beat, but they're an annoyance mainly because their attacks can cause status effects while you're fighting the significantly bigger and more dangerous Devouring Earth.
Those are the regular Swarms. The ones actually called "Devouring Swarms" will literally eat you alive as well as make it impossible to jump, fly, or teleport. Thankfully they only appear in two areas of the game that are totally optional to visit. And they are more of an area hazard saying "don't go here."
Oh, and Rikti monkeys. Evil, evil little beasts.
Don't forget Rikti Drones. No minion should have higher defense than most archvillain have, plus they can see right through stealth and warn everyone around them to your presence. Because just about every Rikti spawn, and every Rikti boss for sure, has one for company they are the bane of any Stalker who enters the Rikti War Zone.
The Red Caps of the Croatoa zone spawn from ambush in annoyingly high numbers, do a lot of damage and have a nasty tendency of turning into harder versions of themselves when you're just about to beat them.
Or the annoying habit of Swarms to wander off during "Kill All" missions, requiring you to search every nook and cranny of the map to find the last one and complete the mission
Both the Cabal and the Circle of Thorns Casters have an infuriating habit of running away as soon as you land a solid hit and never coming back, making you chase after them howling "Coward!" It's a tossup which is worse— the Cabal because they can fly, or the Casters because they lead you into the maw of a horrible Spectral Daemon Lord.
World of Warcraft has quite a few enemies that qualify as Goddamned Bats, although ironically none of them are bats. Many of them are in the Beast classification. You gain only Vendor Trash for beating them, and it isn't long before you don't get any experience from them either. When you're walking around looking for a special kind of wolf to kill, and these 'bats' keep homing in on you, it can get really annoying, especially considering how hard it is to shake an enemy in WOW.
And let us not forget their respawn rate. It's not uncommon to kill one only for another to immediately spawn at the same spot, though it's even worse when they respawn a bit after so you don't see them.
Murlocs. Too social to ever aggro just one, flee when injured to pick up MORE GODDAMN MURLOCS from their stupid little village. And half of them are Shaman with Lightning Shield - fuuuun stuff at low levels. Oh, and they swim. Good luck trying to water walk out to that island for that last bit of exploration when there are like eight million murlocs hiding in the murky water, just waiting for you to leave the shore.
On PvP servers, whatever faction you're not playing may count.
La Tale has literal Goddamned Bats. There is a cave area where these incredibly nasty, powerful, hard to kill bats show up, frequently in swarms, blocking your path to a fetch quest item. Their sonic attacks are difficult to avoid, and running from them is often impossible, as they chase you around, and if you're trying to climb a ladder and get hit by their sonic attacks...
Baol Infiltration Dungeon of Mabinogi. Especially with the Guard Skeleton Hellhounds. They will make you Rage to the fact that your objective to move quietly wont work...
EVE Online has a few of these, most notably Vagabonds and Dramiels, which are bitchy little ships that can outrun you roughly 98% of the time. If you can't outrun them, they'll usually orbit you at just over 10km (right outside of the range at which you can begin to slow them down) and proceed murder you. If you CAN outrun them, then you're probably in a smaller ship, which they're perfectly capable of melting before your backup arrives.
More of Demonic Spiders than they are Goddamned Bats, seeing as they aren't distractions for face-raping, they bring the face-rape. Goddamned bats would be like a fleet of EWAR ships.
The true Goddammed bats of EVE are the little guristas jamming frigates. Goddammed ECM...
Storm Riders in Guild Wars are very strange-looking critters that tend to be fast and have wide patrol routes. Which is itself not bad, but almost all of them are mesmers, meaning they will rapidly stack up a wide range of hexes on the party, and interrupt spells with regularity. And they're fast enough to interrupt spells with 1/4 second cast times. Good luck being a caster against these things.
Arguably the main point of the mesmer class is to be a Goddamned Bat, often not focussing on dealing massive damage but on disrupting enemy attacks, spells and skills.
And most necromancer Minion Master builds are meant to function as friendly factories for Goddamned Bats, not dealing too much damage but giving the AI 10 expendable targets to attack while the Glass Cannon casters hang in the back. The mechanics of creating minions hamper these builds when used by the enemy in PvE and it's not very popular in PvP these days, so you'll rarely face them as enemies.
Stormcloud Incubi in the various dungeons from Eye of the North will strip away any enchantments, causing the victim to be dazed, before spamming high-hitting attack spells. Some groups will add insult to injury by then disappearing for a few moments, confusing your targeting, before dropping back into sight with a fresh set of attacks.
While they might not be something to worry about for most high-level players, Ragnarok Online had places that were full of Goddamned Bats in the form of anything that could use long ranged attacks, given that long ranged attacks cause most characters to flinch for a second, making it possible for other enemies to catch you in case you were running away from them. With the exception of the Swordsman class, that posses the ability Endure, preventing them from flinching, every other character would be annoyingly slowed down in a place that was filled with Kobold or Goblin Archers, mostly when they were running away from a mini-field-boss
There are also Familiars and Drainliars, actual bats that although never the strongest enemies in a map were aggressive, spawned often and common in maps that were frequented by classes that had trouble dealing with them such as healbomb acolytes, mages and dodge-based melee fighters. More annoying was their Demonic Spider cousin the Hunter Fly, which was aggressive, attacked quickly, couldn't be outrun without buffs and often appeared in areas that would otherwise be great low or mid level training spots. They were even patched into many favored leveling areas from the game's beta.
Recently added, Nepenthes, Mandragora's distant cousin. Not only do they have an awful long range and fast attack speed, they also come in large numbers and have a skill that immobilizes you regardless of your stats. To top it off, they'll stop you near a Hillslion, this place's Demonic Spider, extremely strong, extremely fast when attacking and impossible to outrun. If you get lucky, there may be two or three Hillslion on sight to rip your organs off.
MVP mobs are also irritating. Generally, there's absolutely no good reason to take them out, and if they're not beating up on you, they're by their summoner, which will make it harder to aim your skills, or beating up on an ally. The worst part is that killing too many makes the boss summon even more, which in turn makes it even harder to aim or makes you/your ally take on more damage. Flunky Boss at its worst, and it gets even worse than that if the mob is actually dangerous!
Every single creature in RuneScape's Ape Atoll can be stuffed into the category of Goddamned Bats or Demonic Spiders. Set foot on that island and you'll be bitten by omnipresent super-poisoning spiders, perforated by archer monkeys, thrown in jail by ninja monkeys, beaten senseless by ridiculously high-leveled guard monkeys, or attacked and (guess what?) poisoned by undead monkeys. The good news is that there's an item you can get that makes all of these things stop attacking you if it's equipped. The bad news is that you have to traipse all over the place completing Fetch Quest after Fetch Quest just to get the thing.
There are also the Shadows from the quest Mourning's Ends Part II. These things are level 73 but have almost no life points or defence, meaning that they are all offense. Seeing as you need to avoid them while working on an insanely complicated light puzzle that spans multiple floors, they become one of the biggest irritations for anyone trying to complete the quest.
For a literal example of bats, there are the Tz-Kih in the Fight Caves. Letting one hit you drains your prayer, even if they do no damage. Seeing as prayer is your most valuable resource in the caves (which can take hours to get through), it's certainly annoying, though most players will have enough prayer restore potions to easily finish the caves, making them more of an annoyance than anything.
An older example are the wild dogs in the Brimhaven dungeon. They are constantly aggressive to anyone under level 127 (which wasn't even attainable as a level until early 2008), interrupting almost all attempts to fight other monsters in the dungeon. This is no longer the case as of the Evolution of Combat update, which not only lowered their level considerablynote first to 50 and then to 35, but also made every area multicombat, thus eliminating the threat of them interrupting you.
Nearly every monster in the crypts under the Barrows. Most of them aren't any real threat unless the brothers have really done a number on you, but to enter the central room with your hard-earned loot, you have to solve a simple puzzle to unlock the center door. However, being attacked will close the puzzle interface.
Pretty much every monster in Daemonheim classifies as this, especially as of the Evolution of Combat. And yes, on some floors there are literal bats.
The Abyss is crowded with Goddamned Bats in the form of abyssal creatures who pester players that are trying to runecraft through the Abyss, but rarely pose a threat unless they are a low level. Many players even use these creatures for combat training due to their near-endless aggression.
In the action MMORPG Ghost X, there are enemies called Draks, which are man-sized goddamned bats. They most often use their stunning attack, which has deceptively-long and wide range, and the timer for it can stack should you get hit by it while stunned. They often come in pairs or trios, and hang out with large groups of heavy-hitter enemies.
Mission 4 has an entire area filled to the brim with bats, and also a few tough enemies spawn there too.
The boss of Mission 4 is a giant bat, which can spawn smaller bats, which can spawn even smaller bats. The bat-spawns aren't much of a problem themselves, but the boss spawns them when he uses his own stunning attack. The boss also has a very large and very fast shockwave attack, which can easily do 1200+ damage if you forget to attempt to dodge it.
Mission 5 is of high annoyance, due to the cramped areas it has and that they are filled with Draks and many enemies.
Dungeons & Dragons Online has bats which, although quite rare, are decidedly Goddamned nonetheless. They go down in one hit from pretty much any weapon, but you can spend minutes swinging away at them until you finally hit one.
Rust monsters are just as aggravating in this game as in the original pen-and-paper edition. You're best off dealing with them from long range or with a wooden weapon, otherwise you can kiss your hard-earned magical weapons and armor (which are almost invariably made of the metal that they like to eat) goodbye.
Oozes are similarly aggravating. They like to split in two if you try to use a slashing or piercing weapon on them, and they'll quickly wear away anything used to hit them (even wooden clubs) with their acid attack. What they're vulnerable to depends on the type of ooze you're fighting (the Grey Oozes you encounter early on are immune to fire and ice attacks, which does NOT help low-level mage characters who already have a tough time surviving dungeon instances without the requisite spells). Your best shot at taking these things down are with ranged weapons, a weapon you don't mind losing, Good Old Fisticuffs, or a rare crystal Muckbane club.
Kobold Shamans at Elite level know Lightning Bolt, one of the third-level nasty spells, which at the level you first face it at can kill you in two hits if you're a fighter or one hit if you're a mage. And that's not to mention abilities like Hold Person, Web and other spells that your higher-level mage enemies like to sling around later on in the game.
The spiders in the game love to move around a lot and try to get behind you, making melee with them rather annoying.
Rogues cannot sneak attack undead, constructs, oozes or anything else that lacks a discernible anatomy, making these enemies Goddamned Bats to them. Certain monsters also have tremorsense, making trying to stealth past them or get behind them for a sneak attack all but impossible.
Wraiths are completely immune to nonmagical weapons, and unless you have a ghost touch weapon that can ignore their incorporeality, you can count on at least half of your attacks going right through them without even hurting them at all. Their own attacks don't give a damn about your armor, can drain your Constitution, and they have the lovely habit of disappearing and reappearing behind you when their health gets low.
Fortunately all direct damage spells from casters are considered "ghost touch" damage against wraiths. Thus any decent mage or sorcerer can obliterate a wraith with a fireball to the face.
Lord of the Rings Online has a couple of flavors of bats - not only literal bats, but other swarm type mobs like rats and birds that have about half the hit points of a normal mob. They also have a particularly annoying type of mob that likes to follow you and gives you a miss chance debuff, but they don't attack you, unless you attack first. So not only do they annoy you by following you around and not only do they annoy you by making you miss more against any mob you happen to be fighting, but if you mistakenly use an AoE skill, they'll join the fight as well.
Shin Megami Tensei's MMO incarnation, Imagine, has the Inugami; long, floating dog creatures. They're not hugely powerful, but they're obscenely aggressive and attack incredibly fast. Due to this, trying to get through any area populated with them is aggravating, and at lower levels, lethal, due to the facts that they pursue you relentlessly, if you stop to fight them more will usually join in the fray, and they tend to respawn almost as fast as you kill them. At least they have an exploitable weakness to electric moves.
The Vigilant instances in Everquest 2 have Goddamned Bats in the form of Tallonite Kage-Zonns. Invisible until you get right up on them, stun off the bat, hit HARD and FAST (and sometimes multiple times in a single swing). Anything less than a plate armored character is pulp instantly, and even plate armor may as well be cardboard to them. All the trash in The Vigilant is horrible, but Kage-Zonns are the worst...
In Nezebgrad in Allods Online, it's the Goddamned Black Hyena Gang.
Ultima Online has snakes, giant snakes, mongbats, and of course slimes. The first two poison and drop nothing, and slimes destroy your weapon, and split on it. None of them are even remotely challenging but they are incredibly obnoxious because they're everywhere.
Neopets has a flash game that's pretty much your basic Breakout, only with a pair of bats flying around to get in your way. If you're extremely lucky, you can get a falling potion that'll make them go away. But that's rare.
In Gaia Online's Frontier Skies game, there is a random event in which your crew member hears something in the darkness, only to see a vampire in bat form fly out of the ship, carrying off your ammo without even giving you the chance to stop it. (This is especially irritating as ammo is fairly hard to come by once the game gets going, so every bullet counts.) In another random event, your crew discovers that the salt they used at dinner has been replaced with rat poison and lose health while another lone bat flies out of the ship. Vampires will continue to find new ways to screw you over every chance they get throughout the game, and good luck trying to stop them!
Rift has Goddamned Wolves, Goddamned Spiders, Goddamned Undead, Goddamned House Aelfwar, Goddamned Deep Ones, Goddamned Bomani, Goddamned Invasions (which double as The Usual Adversaries)... and the list goes on.
A truly ridiculous number of enemies in Aion have access to the ability "Temporarily Iron Clad", which makes the enemy either invulnerable, or reduces damage taken to single or double digits for about ten seconds. The enemies with this ability have no healing capability, and unless you're massively underleveled, can't actually kill you. In other words, the only purpose of this ability is to drag fights out, making them longer than they should be: if you can do decent damage to the enemy, then TIC isn't going to be a concern, but it sure as hell is going to be annoying when they use it any all of your attacks do essentially nothing, combined with an annoying sound with each hit to boot.
Spiral Knights players have been annoyed by drone-class monsters since the December 19 2011 update. Drones follow a fixed path (unless a breakable block impedes them), inflict Collision Damage (shankles) or status effects (wisps) on contact, are invulnerable until they stop for a brief moment (golden drones never stop), have no damage weaknesses, and drop nothing except hearts or Vitapods (and those drops are very rare).
Champions Online has vampiric bats but they don't really have much in the way of goddamned about them. There are however plenty of other goddamned critters, usually small, often airborne, and hard to spot until you notice yourself being attacked: Qularr firebugs, rats that spawn while you are fighting a manimal rat, demonlings, Destroid gun drones, Foxbattlebot spotlights, Gadroon observers, the smallest Karkaradons, Qliphothic imps, and plenty more.
Dynasty Warriors Online has mages. Mooks are easy enough to kill in the game, but these enemies use an ice elemental ranged attack, which means it can end up freezing you, making you helpless for the duration, which can be a death warrant against an enemy commander.
In Kingdom of Loathing, there are the Irritating Series of Random Encounters in the Penultimate Fantasy Airship, whose name parodies this trope. They appear frequently in this zone, but they drop useful items and experience, making them more of a reference and not an actual instance.