Frankenstein's Monster for the Atari, as seen here, 9 minutes and 40 seconds in, "Look at all these goddamn bats!"
A game called Pharaoh's Curse for the Commodore 64 has a very pesky bat (or is it a bird?). It doesn't kill you at all. No, what it does is swoop down, pick you up, and carry you to a random spot, forcing you to drop any key you were carrying, leaving yourself unable to open the locked door you were planning to. Of course, you can only shoot sideways, so you would be often helpless to avoid it when it swooped down from above at high speed.
Some segments of Viewtiful Joe feature annoying swarms of infinite robotic bats that stick to you, stunning you, and explode unless you button mash them away. They make you solve puzzles slower, and allow other enemies to hit you, but can be fended off with a Hurricane Kick.
There's a certain type of robot enemy in Wario Land 4, found only in Hard mode and above which pretty much covers this. It's what appears to be some kind of metal bird creature, flies in the air right near platforming sections and charges at Wario when he gets near. Not hard to defeat (one hit kills it), but considering that it's found in narrow spaces, doesn't give you anything for killing it, and respawns when you re enter the area, even though every other non transformation enemy doesn't come back unless you win/lose the level, it's freaking annoying. Plus, Pinball Zone (yes, that Pinball Zone that named the trope) is annoying enough without them.
Trine has literal bats that: Always appear at the worst moment (like when you're trying to avoid falling into a Bottomless Pit), always travel in packs, are hard to hit (only one of the characters has an air attack) and deplete your Health Meter very rapidly.
Donkey Kong 64 gives us Purple Klaptraps. These things will chase you down if they see you, and are immune to all your standard attacks. There are two ways to kill them: orange bombs and your instrumental attack. The former is horribly inaccurate, and can actually hurt you if you aim it wrong. The latter is the rough equivalent of using a nuke to kill a squirrel. The fact that these things don't drop health when you kill them does not help.
Crystal Caves has the birds (in underground caverns??) who fly high up, beyond the reach of your horizontally-shooting gun, and bombard you with hard-to-dodge eggs. And the eggs remain on the ground for a while after they fall and crack, and can harm you when you step on them. And sometimes they hatch into another, smaller bird when on the way down.
The Snuggle(?) Bunnies in Nicktoons: Attack Of The Toybots. They spawn in about groups of two or more, are small and difficult to hit, and once they see you they'll try and cling to you, rendering you unable to attack. If you don't managed to shake them off in time they'll explode, flinging you merrily into the air, and often off a platform.
Bug!! With six worlds, each world is bound to have one:
Insectia: Bees. NOT THE BEES! The first Airborne Mook that Bug will encounter, they will try to swoop in on Bug at an awkward angle, and Bug will have to time his jump exactly in order to beat them. Some of them even come in from nowhere, just when you thought it was safe!
Reptilia: Army ants. As in, ants that drop via parachutes, wear army hats, and fire bouncy grenades from their tails. The main problem is that they tend to be positioned at the top of an incline, makign it hard to dodge the grenades.
Splot!: Frogs, frogs, and more frogs. These things jump quite quickly, take three hits to die, and their tongue attack has good range. There are also literal lightning bugs, another Airborne Mook that attacks from an awkward angle to hit and fires out a stream of lightning at the floor.
Quaria: Sea worms move quite fast (especially when they start rolling when you get near) and take five hits to die. Fire-breathing moray eels are also very annoying because Bug starts out so far from them and will have to get closer while avoiding their fireballs.
Burrbs: Snow fleas. Some just jumped out of the floor here and there. Some jumped out of the floor and threw snow at Bug. Some stayed at one point rolling snowballs at Bug until Bug got near, at which they ran away. And the worst kind were those who assaulted Bug with snowballs from a distance!
Arachnia: Green Flies that vomited a pool of acid on the ground. They came in large numbers from offscreen. Also, there were spiders who rolled bowling balls at Bug. Not too bad on level ground, but they usually did it from the top of a slope...
Taz-Mania for the Sega Genesis has the goddamned Bushrats. They're almost impossible to jump on due to their size, they throw spears at you, they can cause you to accidentally spin away health powerups in the process of killing them, and they can also cause you to spin off a platform and into oblivion.
Also, the actual bats in the ruins levels. They can camouflage themselves against the dark background to make themselves harder to see.
Mario vs. Donkey Kong has certain levels that feature an invulnerable bird that flies back and forth and drops eggs. If the bird or one of its eggs touches Mario, he loses a life, forcing you to restart the level from the beginning, and unlike other Mario games, the bird can not be defeated by jumping on it. The levels it appears in are considerably more frustrating than they reasonably should be.
The Batabats in Atlantis no Nazo fly so high the player can't even touch them and throw down triangle-shaped droppings. They're the first enemy encountered in the game.