Despite the JRPG makers vying for this prize, I have to say that Bethesda leaps in and steals the prize from my hands. I usually hate little boys (Mack, Ventboy, that **** from Infinite Undiscovery, Hope if he can still be classified as a kid etc) way more than I hate little girls, however Bethesda's children (see Little Lamplight in Fallout 3, general kids in Skyrim) are so horrible that my Good character ends up chasing them with a flamethrower.
I'd have to go for the children of Assassin's Creed 3. Flocks of them will swarm around you and blow your cover by laughing and running around you, and you can't kill them because they're children. The residents of Little Lamplight are a close second though.
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Can anything really top the annoying children of anime?
Well, the mayor of Little Lamplight, who is at most 11 years old, routinely threatens a Power Armor clad Wastelander carrying a mini nuke launcher and there is no option in the game to shut him up. He is like the incarnation of every annoying snot nosed brat on XBL and every single line he has induces "Punch him in the face"-syndrome.
If you have played Mass Effect 2, he is like Aria, except 11 years old, with no connections or armies behind him and armed only with a gun that can't even begin to touch late game armor. Unlike Handsome Jack he isn't even funny, just obnoxious.