Anything with an Ion Disruptor in X3: Reunion. This weapon is extremely effective against shields, automatically locks on to anything in a wide fire arc, and has no travel time. While it can't damage your ship's hull, it is extremely effective against shields and can destroy equipment once your shields are down, as well as making you easy prey for lasers, missiles or collisions. Since all ships are susceptible to friendly fire, even friendlies using the Ion Disruptor turn into Goddamned Bats. As if it wasn't already annoying enough, using the weapon yourself when there are non-player-owned friendlies around turns you into a bat, and they'll instantly attack you.
Kha'ak fighters in X3: Terran Conflict qualify for capital ship captains. Individually they're no threat at all since a few good flak hits will splatter them, and their weapons are really weak. Clouds of them can wear you down. Oh, and they spawn continuously as long as you're in a Kha'ak sector.
Kha'ak clusters in general. They're made of a Kha'ak M3 and a whole lot of M5s. They all have Kyon Emitters, but those do so little damage that they're no real threat to anything with more than 50 MJ of shields. However, the M5s are going to be faster than anything you have, and so it turns into you flailing around trying to swat the little bastards before they can kill you via Death of a Thousand Cuts, unless you have a Plasma Burst Generator or Phased Shockwave Generator.
M5 scoutships in general, but particularly the Teladi Harrier (although it is unusually slow for its class, since it's a typical Teladi craft), Yaki Fujin, and Xenon N (the only common M5's with credible weaponry). They come in swarms (often alongside ships that actually pose a threat), and, unless you have Hurricane, Wasp, Rapier, and/or Disruptor missiles, they are too fast to hit with most weapons. Get enough in clear space and you basically need a capital ship's flak guns to clear them all out.
Here's one from an old-but-good flight sim, Total Air War: any form of antiaircraft gun. Particularly the ZSU-23-4s and Vulcans. Normally they're not a threat if you fly high or if you're packing guided missiles, but when some bright spark in mission control decides that the best way to use your F-22 is to load it with unguided bombs, rockets, and cannon shells, all of which require that you fly low to attack with any kind of accuracy, those AAA vehicles with their mixture of More Dakka and Improbable Aiming Skills can and will turn your aircraft into shrapnel. And worst of all? They're everywhere!
In the Ace Combat games, normal mook planes and SAMs become annoying when you need to kill aces while they're around. They may ascend to Demonic Spiders level in Ace mode, where a single missile hit will almost always destroy your plane. The ballistic missiles in Ace Combat 04 are just really annoying to shoot down. If you watch the flight path replay at the debriefing, you'll notice they goes side to side and up and down in a sawtooth pattern. Even the Game Breaker QAAM missiles have a hard time with this one.
The drones is 6. They are more maneuverable than the enemy aces.
The Naval Ops series has PT boats, tiny little things that are no real threat to a larger vessel and which usually go down with one good shot from your main guns. Then you meet the advanced versions in your second playthrough, who carry lasers and shields and cannot be locked onto. Both types are fast enough to be tricky to hit.
In Animal Crossing catching certain very common fish and bugs is this. Sea Bass in particular are a well known annoyance, as on most days other than rainy days you'll probably catch them much more than the fish that are actually worth anything. Mosquito's are a more straight forward example of this trope though. They are attracted to you instead of running away like most other insects, so if you're fishing and it bites you the player reels in their line causing the fish to disappear.
Every Mech Warrior game has the Elementals. They're light powered armors that zip about the battlefield and do their best to dent your Humongous Mecha's armor while running circles around you. Individually insignificant, they nonetheless represent a threat in groups and their diminutive size makes them a massive annoyance to get rid of, requiring either lots of laser fire in the hope of eventually hitting them or the expenditure of precious guided-missile ammo.
Mech Warrior 4: Vengeance gives us the Uziel. A Medium 'Mech that carries short-range missiles, lasers, and a pair of PPCs that can cause an Interface Screw. The level designers must have had a subconscious attraction for the 'Mech, as you will encounter lots of them over the course of the game's campaign.
Hardwar has the pirates. They're (mostly) lightly armed so they don't represent a significant threat individually (unless they're carrying FireBurst or Groundbase missiles), but they're everywhere, and they'll drop whatever they're doing to attack you if you're carrying so much as a few pieces of scrap metal. It doesn't take long before killing them by the dozen becomes a routine action during every cargo trip.