Any character who is controlled by an AI, tbh. Mass Effect springs to mind. I can't count how many times I've been trying to shoot an enemy and then suddenly a character walks straight infront of you, blocking your path, and you end up getting shot by the enemy when trying to move so you can shoot. Oblivion springs to mind also, when your working along side guards, and the guard suddenly gets in the way of you, and you end up hurting the guard instead of the bad guy, causing the entire brigade to come after your head instead of the enemy.
Navi is the character I instantly thought of when I saw the topic title. She wouldn't of been so annoying if she only said what she had to say once, but then she keeps repeating "Hey!" "Look!" etc and it just gets annoying.
Like others have said, Roman from GTA4 was damn annoying. You're driving along, going to do a mission or something, and suddenly you'll get a phone call from him, with his annoying accent. It wasn't be too bad if he only phoned you once in a blue moon, but when he phones you nearly every day, it gets beyond annoying.
Piros from Hack annoyed me, he reappears on GU too. Mainly due to his annoying voice and the way he speaks. HE OF FAIR BLUE EYES!