The Goddamned Like-Likes in nearly every freaking game. They eat your shield, sometimes for good, have ludicrous amounts of health, and are extraordinarily hard to avoid at times.
Although, The Legend of Zelda: Ocarina of Time makes it (most of the time) so you can kill them from a distance. The only times you have to fight them head on is in the Spirit Temple and the Gerudo Training Ground.
Suspiciously absent from The Legend of Zelda: A Link to the Past (Though they were reintroduced in mercifully small numbers in the GBA remake), that job was instead filled by Pikits, which could do everything Like-Likes could at range. Later games introduced Rupee Likes, which stole money instead of shields, and disguised themselves as Rupees.
Wall Masters, in all incarnations, have the power to send you back to the beginning of the dungeon you're in, which is every bit as annoying as it sounds. Not to mention that they drop from the ceiling, climb out of walls, or extend from pools of shadow, making it easy for them to catch you by surprise. And they're really creepy.
Worse yet, some traps release invisible Wall Masters. Fake Difficulty at its finest!
And worse, the Floor Masters, which cross the line to become Demonic Spiders. They can turn temporarily invincible, are sometimes invisible, stun you, and split into five smaller floormasters that regrow into the full-size version if you don't kill them fast enough. In Wind Waker they're essentially floor-bound Wallmasters that warp you around. They're very fun in the Earth Temple, where they're often hidden by clouds of fog so you walk right into one and are grabbed before you even know it's there, where said fog actually stuns you so you can't use any items, and can grab nearby skulls, vases, etc. and throw them at you. And then there are the parts where you have to control Medli through these, because if they grab her, you have to run all the way back to the beginning of the dungeon just to get her back, and has utterly no way of defending herself.
The Skultullas (all types)— with the exception of Gold Skulltulas, which are the direct OPPOSITE of goddammned bats.
The Keese (literal bats) and Bubbles (flying skulls). While Keese were merely typically erratic and annoying flying enemies in the 2D games, the 3D games made them model examples of frustrating little a...well, you get the idea. First off they are an immense pain when you attempt to lock on to anything else (or manually aiming for something in 1st-person mode, which will often prompt them to swoop up on you from behind for a cheap shot), as half the time you'll end up targeting an out of range bat, which allows the nearby ground enemies to eat you alive or fall off a ledge while you attempt to target something else. Second, they are often wrapped in magical flames, meaning that you'll be walking along and suddenly get set on fire, cursed (unable to use weapons), or frozen solid in a giant ice crystal when one hits you (and then skitters out of range while the effect wears off). Third, they love to hang around underneath tricky platform segments and behind climbable objects, often swooping in to knock you off at a critical moment.
In Ocarina of Time, you get a spell called Din's Fire, that expands in a sphere, damaging many types of enemy you run into. Keese, however, aren't fazed by it: instead, they catch fire, becoming the aforementioned burning Keese (who can not only set you on fire, but burn up your wooden Deku Shield). Fire arrows are not recommended either (as Awkward Zombie demonstrates).
The Game Boy versions also had bats, which often would let out a rupee. For greedy players, this would get endlessly frustrating when the rupees would end up three tiles into a cave wall.
Other enemies acting exactly like Keese are Guay (Like Keese, only outdoors) and Bad Bats (Like Keese, only bigger.)
In any of the 2D games, Wizzrobes hang out in groups of three or so, teleporting randomly around the room and sending off magical bursts before disappearing once more. You kill them by getting behind them and slashing their behinds — assuming another Wizzrobe doesn't appear behind you and fry your tush. There are two kinds: the orange ones, who are the teleport-happy dicks; and the blue ones, who are Demonic Spiders.
The Wind Waker Wizzrobes teleport, can summon more enemies, and laugh at you. They even made a Room of Doom out of them, where there were 3 Wizzrobes who continuously spawn monsters. If you don't kill them off immediately with ranged attacks, you'll never have the chance to again.
They themselves can't hold a candle to the Wizzrobe boss who had all of the aforementioned abilities, as well as being able to summon more wizzrobes who could in turn continuously summon enemies (including keese and bubbles), leaving you quickly fighting a small army of Bats.
The combination of Wizzrobes, Bubbles, and Like-Likes in Zelda 1 that introduces you to true terror. Wizzrobes teleport and shoot a lot. For later reference, what they shoot can only be blocked by your special magic shield. Wizzrobes can only be killed with your sword and bombs (the wand's melee effect doesn't work on them). Bubbles take away option 1 whenever you hit them, as they make it impossible for you to use your sword for a time. Like-Likes will grab you; the only way to escape is to cut them open from the inside with your sword. And if you don't do it fast enough, they eat your magic shield, which was the only thing that made fighting Wizzrobes even possible. So if a Bubble hits you and knocks you into a Like-Like, you're basically screwed. Oh, and the game absolutely loves putting groups of all three monsters in the same room towards the end of the game.
The wizzrobes in the Game Boy games especially fit this, as there was a very slim time during which you could hit them. You had to dodge their beam, get to the side of them, and then slash away at them, and if you missed any of those three steps by so much as a pixel or if you took too long doing it, you had to wait and try again. All this, combined with the fact that they usually appeared three to seven squares off made rooms of them tedious, but not really difficult. It's even worse than that in one Game Boy game. Link's Awakening Wizzrobes do all this teleporting, and can only be defeated by bombs.
In The Legend of Zelda: Four Swords Adventures, the Wizzrobes return, and become a massive nuisance because of one simple thing. They can drain Link's collective wallets dry by stealing Force Gems, of which you need 2000 to complete the level. And these flee from Link rather than stand still like the fire throwing Wizzrobes. Fortunately, in most cases, destroying them frees up most of the Force Gems it took. Keyword being most.
Don't forget Leevers. They appear from the ground, slide, and hit you, and never stop coming. In Ocarina of Time, killing enough makes a gianormous Leever appear.
ReDeads paralyze Link with their scream and then proceed to hump him to death. See here. In Ocarina of Time, Nintendo really screws you because the marketplace in the future is full of these things. You can play the Sun's Song to turn the tables and paralyze them instead— too bad there's no such song in Twilight Princess. They also ramp up the annoyance by carrying around a rusty BFS that they smack you with after paralyzing you with their scream. There's a part in the Desert Dungeon where you face two of them at once while a swarm of tiny skeletons with tridents try to skewer you at the same time.
Peahats fly around in the air attacking you. In the first game they're completely invulnerable unless they stop and land, and then only vulnerable for brief periods so you need to try hitting them while dodging the other 10 on the screen. The ones in Ocarina of Time were no less annoying even given the ability to attack them in the air.
Even worse were the Nightmare Fuel Seahats in The Wind Waker. Hope you like falling out of your boat!
Twilight Princess and Skyward Sword render them completely harmless and even helpful (as Clawshot targets).
They're annoying in The Legend of Zelda: The Minish Cap too, where they're completely invulnerable to your sword, and often found in places where you need to use an item other than the boomerang or gust jar that works on them.
The Legend of Zelda
The RED EFFING BUBBLES from the original game's second quest. Get hit by one, and you permanently lose the ability to use your sword. There are only three ways to regain it: Find a Blue Bubble and get hit by it, drink the Water of Life or visit a Fairy at an Overworld spring (that last one is a bit difficult since Bubbles are only found in the labyrinths).
Pols Voices, the hopping bunny ghosts that hates sound. In the original Legend of Zelda, they're buggers who love to swarm the screen and hop into Link, trying to deal damage. Of course, they can be dispatched with one arrow (or later on in the series, any musical instrument). What's worse is they hop around the screen rather quickly, qualifying their status as Goddamned Bats. In the second quest, Level 2, you have to face them with the sword, and they take about five-eight hits to kill. Fun if you're not at full health.
They were much easier to deal with in the Japanese version, as the Famicom controller contained a built-in microphone, and yelling into it killed them instantly (this is what the manual meant by them hating loud noises). NES gamers had no such feature, making it much more difficult until you figured out their weakness to arrows (and confusing anyone who tried to kill them with the Flute).
Unless you have the sword beam, Darknuts are a torture because they can only be hit on the side and back. To make matters worse, Link's tank-ish control will cause him to get hit once in a while. They also take a long time to kill.
Zelda II: The Adventure of Link
Aches (little blue Goddamned Bats) in Zelda II: The Adventure of Link are very often placed so that they sweep across lava/water pits, knocking you to instant death. If you try to kill them you'd better hope that you can get them to sweep at you without jumping across the pit, because even if you do manage to hit them in mid-air, the odds are very big that you STILL fall in the pit because of the slight pushback you suffer from just hitting things with your sword, which will cause you to stop in mid-jump so you fall straight down.
The ubiquitous knife-wielding Wosu from the same game qualify. They cause a pitiful amount of damage if they touch you, but they knock you around a bit and steal your EXPERIENCE POINTS, which becomes worse the later you get in the game.
The Mobys, the birds that drop down from the sky and come charging at you. Like the aforementioned ratmen, they steal experience if they hit you, and the experience you get for beating them is paltry (still better that the ratmen, who give you nothing). They truly never stop coming at you; once one is beaten or leaves the screen, another immediately follows. They also love to come at you in the swamp, where your movement is hindered and thus so is your ability to avoid them.
Two towns in the game (Saria first, then Darunia later on) have monsters disguised as townspeople. Anyone Link talks to that doesn't have anything significant to say presents a random possibility of turning into an ache afterwards. They can be defeated, but the amount of health the bats have seems to be COMPLETELY random as well...sometimes the bat will go down in one hit, sometimes the smug little jerk will take QUITE a beating to finally destroy. The problem with that? They're still worth no more exp than the "one hit wonders" versions.
The two different animated head statues, Ra and Mau. (Ras are the dragon-shaped ones, Maus are the panthers). Both spawn infinitely and drain experience when touching Link. Ras double as Ledge Bats, Maus basically Zerg Rush Link. Another annoying monster of a similar nature is Bago Bago, the skull-fish that appear on bridges. Like the aforementioned monsters, they spawn infinitely and drain your experience when they hit you. To make things worse, the variety found in the Great Palace also spit fire at you.
Another example frustration from the Zelda Game Boy games comes in parts involving platforming and standing on moving platforms...when all of a sudden Keese appear, and both hurt and push you into spikes/pits.
Ocarina of Time
The Shell Blades in Ocarina Of Time are this type, they tend to swim up and attack Link aggressively, while you can only use a hookshot on them, and hope you get past their hard shells to their ONE Weak Spot.
The Bari in Ocarina of Time. Floating Jellyfish that are immune to the slingshot and hurt you when you kill them with the sword. That leaves four options of killing them without getting hurt: Din's Fire (which many won't have at that point and wastes magic), Deku Sticks (which break and are in limited supply in the dungeon), the Boomerang (which you don't get until halfway through the dungeon), and Princess Ruto (yes, you can use her as a projectile and it won't hurt her one bit).
Also in Jabu-Jabu's Belly are Shabom, large kamikaze bubbles that reflect most projectiles, and Stingers, large flying fish that stalk you as you move around. Like the Bari, however, Shabom are also very weak against Deku Nuts.
The Skullfish in The Legend of Zelda: Majora's Mask counts since they're virtually everywhere in the Great Bay and can come out of nowhere. Plus, the only way to kill them in the water is with Zora Link's electrical shield.
The The Legend of Zelda Oracle games manage to avert this trope quite well on the other hand. Wallmasters and Floormasters are significantly easier to dodge and destroy while other enemies are easy to kill or few in number. Like-likes still suck.
The Wind Waker
The Blue Bubbles from The Legend of Zelda: The Wind Waker. Because getting hit with one keeps you from using items for a while, you have to put out the flames first. The only way to do THIS is with ice arrows, your deku leaf, or the hookshot. Easy enough, except in a certain few rooms in the Wind Temple. You have to get from a lower level platform to a higher one to advance. The only way to do this is by hopping from a series of platforms across a non-bottomless chasm. You can't do this without controlling Makar to have him plant trees that you can use your hookshot on. The room is full of them, bobbing along above you. This makes the deku leaf worthless, because it only works on a vertical platform, leaving you only ice arrows. However, because of the sheer number of Wizzrobes in the dungeon, you're low on magic and arrows at this point, and the Bubbles are moving, and sometimes even blocked from view. Once you DO manage to get one, it falls into the chasm, which you have to jump down to and kill it BEFORE it becomes unstunned and the flames return and it flies back up so you have to do it all over again. If that weren't bad enough, they jerk you out of controlling Makar if they hit him, causing him to fall to the bottom of the chasm, where infinitely regenerating grabby-claws mean you have to hop down, cut him free, and carry him to a safe location before you can do anything else.
Thankfully, while you still have to deal the final blow if you use the Hookshot, a good aim can make the whole business moot, since doing so both draws the Bubble toward you and instantly puts out its flame.
Ocean Octoroks in Wind Waker seem to know when to show up so it can maximize its annoyance factor. In fact, pretty much any sea-born enemy in that game is a pain in the ass, such as the Gyorgs— once they start following your boat, manoeuvrability goes down the toilet. Not to mention what happens if you get knocked overboard. Sea Octoroks are particularly bad though because if you're in a place where they happen to hang out? They never. Stop. Fucking. Coming.
Miniblins in Wind Waker. Little devils (literally), complete with pitchforks and ears just as pointy as Link's. They attack in swarms, making indescribably annoying sounds and jabbing you with their 'forks.
In some areas of Forsaken Fortress and other areas, they literally spawn infinitely...from Hammerspace.
The ghost rats from The Legend of Zelda: Twilight Princess are invisible (and unkillable) unless you're in Wolf mode and using your senses, and while they don't do any damage, they reduce your movement to molasses on a cold day WITHOUT ANY APPARENT REASON. This turns into a nightmare in the Bonus Dungeon when you're dropping in on a room of difficult enemies and you inexplicably find yourself moving incredibly slowly while getting whacked to death, and then you have the hassle of becoming the more vulnerable wolf to kill the rats, all the while taking damage from the REAL enemies.
And also typically the rats slowed you over quicksand in the first dungeon you meet them.
In a less annoying fashion, the same dungeon that housed the ghost-rats also had huge swarms of (thankfully visible) insects that would cover Link and crawl all over his body (with Link looking only mildly creeped out by this). This was really only a case of bats in rooms that also had quicksand, where stopping to swing your sword and knock them off might slow you down enough to sink into the sand if you aren't quick enough. Thankfully they flee from a lit lantern.
This game's ReDead Knights can prevent you from obtaining Chu Jelly, your only source of health in the Bonus Dungeon...And losing good Chu Jelly because they stunned you isn't the worst part of it; if they paralyze you, you will have mash buttons or get whacked; however, that doesn't prevent other ReDead Knights from screaming and putting a whole rinse-repeat on the process...
The Yeti's house in Twilight Princess is infested almost exclusively with this enemy type.
Poes in Twilight Princess are extremely aggravating until you obtain the Master Sword and gain the ability to shift between human and wolf form at will. You can only see (and kill them) in wolf form, but for the first half of the game, you only ever run into them when you are in human form. Your only choices are to run away or get beat to death by a floating lantern. It is extremely cathartic the first time you run into one in wolf form and get to rip its soul out with your teeth!