As seen above: GTS asshats. "If you give me a Level 9 Haxorus, I'll give you my level 5 Snivy!" or, just as bad, the high-level-rare for low-level-common turds. "GIMMIE YO LEVEL 100 MEW FOR MAH LV 1 BIDOOF! NAOW!". The GTS is a joke. They should really put some sort of restriction on it so that things like my examples don't happen.
NPCs that decide to move when you move, especially the ones that move RIGHT INTO your path or the trainers that you think are stationary until you move, then they turn to face you...and, the girl in RGBY who says "Eeeek! Did you just touch me!?" Um, no. I was on the opposite side of the screen trying to avoid you...
Metronome...I have the worst luck ever with that move. Everyone else gets something cool. What do I get? Sand attack, Leer, Growl, Tail Whip, Screech...sometimes I get Explosion. I hate explosion and self-destruct. That's why I never use them. I just think it's stupid to make your own pokemon faint for a chance (a mere chance!) to faint your opponent.
Recoil moves. Hate them. I also dislike Hyper Beam and its variants (you know, attack this turn, but you can't do a thing next turn).
Trainers with 6 Magicarp, Caterpie, or other weak pokemon--especially when they are at high levels. Y U NO EVOLVE THEM!?
And finally, Sturdy, as so many of you have said.