Those flying enemies in God of war 1. The ones that swarm around your character in swarms of close to a hundred slowly chipping away at your health as you desperately try to fight off other enemies. In the battle near the end of the temple where there was the fight on the conveyor belts as hundreds of them attack you along with stronger enemies, I was just about ready to pull my hair out, make a rope, and strangle myself with it... and this was on normal difficulty!
Other less annoying but still annoying enemies: Enemies in Final Fantasy style games who insist on not dropping items you need from them even after you've butchered your way through entire ecosystems, had a REAL special time with them recently in Lost odyssey; jackal snipers, non-jackal snipers, snipers in games in general; overpowered single enemies you have to burn through half of the universes ammo just to make them say "oww, thats going to require a nasty plaster" I'm looking at you Bungie! Tartarus was not enjoyable to fight, just annoying! Invisible enemies, or that annoying type of enemy that stands back and hits you with really powerful weapons from a safe distance while you're fighting some really stupid, fairly harmless enemy which doesn't do much damage but who has a lot of HP and who you can't get past. ANY enemy who attacks me after a really hard battle that's reduced my health to a sliver and kills me in my weakened state (grunts killing me after I've taken down a white elite and about half a dozen of his cronies for example.)
On the strategy games front: skirmirshers, simply because they have no point beyond getting in the way of my other troops as they butcher their way through the enemy lines. There's nothing worse than having a group of sissy skirmirshers rout suddenly because the enemies cavalry looked at them the wrong way and having the whole army get demolarised and run after them. We have archers for ranged attack, so I ask you: skirmirshers, what is the point in them? Mangonels in Age of empires 2 are also REAL fun to deal with. Its so nice to see that wonderful army you've constructed thats been carefully constructed to balance in all situations, with really high tech weapons and a lot of very expensive knights get tanked by twelve men and a handful of siege weapons.