BlazBlue's "Unlimited" Rachel can summon a Frog. It's easy to overlook, shocks you for multiple hits if it connects and unlike her regular frog, doesn't vanish after a hit so you just keep taking hits from the frog while trying to handle all Rachel's other attacks.
Glire, Glice, and Glunder all attack you in a disproportionately large proximity to them with elemental discharges. Glice, in particular, can chain freeze you to rack up damage quickly unless you struggle to break out.
Floow have a nightmarish shriek that causes damage despite your shield, chase you everywhere, and regenerate when not under direct aggression. Furthermore, elemental attacks (like PK Fire, given you're playing as either Lucas or the Pokémon Trainer when you first find the bastards) don't work at all. Cluster frag the bastards if more than one come at you.
Armights have a creepy laugh when they arrive on the scene, slash at you in a close enough range (which is longer than most characters can reach) and throw their swords at will.
Mites do pretty weak damage, but their vast numbers can overwhelm you and deny you a chance to counter if they're feeling particularly vicious. Their small size makes them a little harder to hit. And in hard mode, they can knock you across the third of the screen, and have a much higher damage output, making them even more annoying to deal with.
Bytan is another swarmer, spawning more Bytans by popping them out of its eyeball, meaning that anywhere that starts with more than one bytan essentially promises a swarm by the time you're done. Unlike the Mite, they deal normal damage. They also come in a giant version that can take a crazy amount of damage.
Buckots. They swoop in when you're fighting other enemies and dump hot bricks on you. It's annoying. Plus, they fly, so they can be hard to hit sometimes.
Bucculus, which lurks in the ground where you can't hit it, mostly hidden, and latches onto you when you get close. The worst part is that if you don't kill it quick, it goes back underground, and you have to lure it out again by getting within grabbing range once more. The worst part is when they're in an area you haven't been to before, because you don't know where they're buried and might be looking at something else rather than watching the ground.
Roaders are very fast so it's hard to get a hit in first (if at all), come roaring off from the side of the screen so you never know what's coming until you've been smashed into a bloody pulp, and have huge knockback. Oh, and think you can beat them because you're on a platform out of their reach? The bastards can jump. That's right, an armored, motorized unicycle can jump to get you. Being stronger than most enemies listed here, they wouldn't normally be under this trope, but the fact that you run into them so often (and sometimes in groups too boot, especially on higher difficulties) makes them annoying enough to mention.
The Guilty Gear series contains 3 examples of this: Bridget's teddy bear, Roger, almost all of Zappa's summoned ghosts and any of Dizzy's projectile attacks. Admittedly, I am almost always on the giving end of this, but the murderous looks I receive from my opponents (my friends have all but refused to play against me if I choose to use any of the aforementioned characters) upon their defeat is the main impetus for their inclusion here. Oh yeah, I almost forgot: Eddie/Zato-1 is the very personification of Goddamn Bats (in my opinion) and often causes me to be the the one giving my opponents looks of murderous intent. And Chipp is no slouch, either.
Eddie is considered God Tier for a good reason. He fills the screen with so much crap your opponent simply cannot do anything without getting hit.
Where does that leave Zappa? He uses a possessed cleaver, a shadow dog and three ghosts that follow him around and can curse an opponent by going to him. And once he gets Raou, all hell breaks loose as it even grants Zappa an unblockable super. Zappa is one walking Goddamned figther, especially when used properly.
The Gadget Drones in Magical Battle Arena. Their attacks are slow and weak and they die from one or two special attacks; however, their attacks can still interrupt you while you're charging, they come in swarms that pepper you from many directions, their concentrated fire can break you out of your super, and they accompany That One Boss and the Final Boss. Few things are more annoying than getting struck by one of their stray shots while in the middle of attacking or running away, leaving you wide open for the more dangerous boss to pummel.
Not to mention you face three of them on the first level, where you're also expected to get used to the controls. Learning how to play a game as technically difficult as MBA while having your character interrupted every half a second by a stray shot (not to mention the occasional "rush up, combo yo' ass and send you flying to the pavement" attack) is just about as impossible as it sounds.
The tanks in the PS2 version of Godzilla Unleashed. They're tiny so they're hard to destroy, and sometimes they're virtually impossible to see... especially when they blend in with the rest of the scenery. To make matters worse, they attack you at the worst possible moment (usually when you're trying to use a beam-attack or are about to throw an enemy) which slowly but surely drains your life-bar. Oh, and they constantly respawn, making them even more aggravating. The ONLY way to escape the tanks is to go into deep water. Unfortunately, apart from a handful of levels, this is easier said than done. Tokyo and the Mothership are the only levels not to feature the tanks: unfortunately, the Mothership replaces the tanks with the equally-annoying saucers.