Already been mentioned tons of times, but perhaps that's a sign of just how annoying they are. Escort missions, and missions where you have to take care of someone in general. It's been a complaint that's been seen over so many games now, and it's often one of the biggest complaints I've heard about the old Nintendo classics. Star Fox and Goldeneye are both widely appreciated games, but both have parts in which you have to take care of others (I believe it's actually constant throughout Star Fox, since I always hear about how people hate Slippy ;p), and in Goldeneye it was during one of the hardest missions in the games, so yeah. Someone mentioned somewhere, that they found escort quests where you had to carry the escort much more tedious than when they follow you around, in reference to the Earth and Wind temple in LoZ Wind Waker (I believe I've mentioned this game in all of my posts in here today now xD), but I honestly much preferred that over having some bad AI following you around at an incredibly slow pace, getting stuck in walls, and just standing around getting shot at without heading for cover. Ellie from The Last of Us is a good example of some semi-bad AI, since she constantly kept swapping around covers, and she was generally just annoying iirc. Definitely not on scale with some other things we've seen before though :p
And fetch quests... There's nothing worse than having to traverse the entire world, or having to kill hundreds of enemies just to get certain items for a quest. I mean it's an easy concept to grasp, and might be a bit entertaining in the beginning, but it's a huge cop-out, since it's basically just there to prolong the experience, even if it might not be the most entertaining.