Is it sad that I when considering my answer I immediately thought of various GM NPCs who we loathed with a passion, rather than any splendid bit of RP by a GM or splendid bit of characterisation by a scenario writer?
The main culprits were:
1. Nathaniel McElephant, unkillable, bossy, combat monster paladin in a very loooooong D&D campaign. Even his sodding horse was better at combat than we were, and immune to all sorts of magic, etc. His surname wasn't really McElephant. But he returned to his home village at one point in the campaign and came back to the the party announcing that he had a son, and we should celebrate with him. At which point I said "Er, but you've been on this quest with us for 2 years..." and another player replied "Elephants have a gestation period of 2 years." So we referred to him as McElephant from then on. Two of us players hated him so much we refused to take part in the end level boss fight, after he teleported us to another bloody continent specifically so we'd do what he wanted us to.
2. Dr Orient. In a series of CoC one-shots and mini-campaigns. On the face of it, this NPC was just the standard "little old man who points you at the plot" trope. However, the GM ran him as all-knowing... but never telling you anything bloody useful prior to the adventure. We'd stagger back from a fight with a werewolf, covered in bites and half dead, only for him to say "Hmm, yes, I suspected it was werewolves. The area has been prone to them for centuries." One session the GM began by announcing we'd had a letter saying Dr Orient was dead. I don't think he was expecting such a resounding cheer from the players! He was indeed dead, but his bloody ghost turned up.
3. That Bloody Silver Fang in a Werewolf campaign. Can't remember what the NPCs actual name was. We just referred to him as That Bloody Silver Fang. Bossed everyone about. Kept appearing when we were partway through a fight and killing all the bad guys, thus depriving us of Glory & Honour points. Was nowhere to be seen in fights where we'd actually appreciate an overpowered ally.