Zelda- keese, octorocks, zola, peahats, stalfos, eyebeam, flying tiles
Mario- lakitu, shooting koopas (SMW), rocky wrench, hammer bros., boomerang bros., giant cheep cheep
Donkey Kong Country- the jumping crocs, bees

Final Fantasy: Marlboro
Dragon Quest: Metal Slime

Mario- Cosmic Clones, Octogoombas, Lakitu and Spinys

The Medusa Heads from Castlevania.

Legend of Zelda- like like

Nuff said

Kid Icarus - Eggplant Wizards and Plutons.

Actually, those two are probably the most annoying enemies of all time.

However, if possible, you can kill them from a distance.

Metroids from Metroid are pretty annoying, how you have to freeze them before they rush you and suck your life force.

Cheep cheeps in the Mario series (those red flying or swimming fishes). The HUGE ones that can swallow you up in Super Mario Bros 3, are the most annoying ones.

True, but most of the enemies you listed aren't annoying at all. Like Likes are more trouble than all of them combined.

OTHERS
Zelda- electric disc things, knights in Zelda II

Mario- Lakitus, Hammer Bros., Chargin' Chucks
Zelda- Wallmasters
Kirby- Gordos
Metroid- Metroids
Sonic- Those Spiny Catepillars
Mega Man- Pippys
Duck Hunt- The Dog

Chargin' Chucks are a bit annoying, but are tolerable.

The Dog isn't an enemy in Duck Hunt, silly!

You're mention of the catterpillars reminds me: I hate the cactus enemies in Mario. They're only tolerable with Yoshi.

ZUBAT.

@StarFox - it depends on the definition of the word. Some people are annoyed by the dog from Duck Hunt because whenever you miss a duck (Mode A) or two (Mode B) he'll always laugh at you. You might not be able to shoot him in the NES game, but I can understand how people would find it annoying, the dog's laughter.

Zombie Panic in Wonderland - the crows
Star Wars: The Force Unleashed - Stormies/Mandos with jetpacks
Star Wars: Rogue Squadron series - TIE Bombers when you have to protect something, AT-ATs, TIE Defenders (at least these last ones are only in the last level of the first game)
Super Smash Bros. Brawl - Metaknight Tornado spammers
Mario Kart series - Blue Shells
3D Sonic games - the camera, bottomless pits

The blue shell isn't an enemy.
The camera and pits aren't enemies.

In your eyes maybe.

The word "enemy" can be interpreted in many different ways.

1. No it can't.

and
2. I think Headcrabs from Half-Life 1 and 2 are really annoying. They can jump like 65ft and are pretty hard to hit because they're so small. And they always come at moments you don't expect out of crates, around corners in airvents falling form the ceiling etc.