My one skill was being an obnoxious, annoying pest. I think my most obnoxious character was a lawful neutral wizard who was a stuck-up, obnoxious prig. Lawful neutral meaning all the moralfagging of a paladin but without the moral part. And he talked like a fag too.
Anyway, my one skill meant that my main playing was as a temporary guest player doing the kind of character who would usually be an NPC but needed more fleshing out, often someone who had a critical role to play at some point in the adventure (so they couldn't just kill me) and usually an incredibly annoying prick who would do everything to try to sucker the other characters into killing him.
I had one character who was the stereotypical chaotic neutral fuckwit but knew where the stash was that was the point of the expedition. Within a few minutes I had everyone hating me so much they wanted to torture the information out of me, but the paladin who was the party leader refused. I taunted the paladin relentlessly every time he did his usual lawful goody two-shoes bullshit. Due to cleverness on the part of the players, there was an encounter with another actual NPC who also knew the location, and they tricked him into blurting it out.
Everyone looked at me and I knew what was coming. "We don't need this guy any more, do we?" And I taunted the paladin one last time. "That wouldn't be very good, would it. Would [your deity] like that?" And he rolled a 20 and chopped off my head on the spot with his handy vorpy and said "I'll repent tomorrow." And we all laughed.
But you can see how this kind of behavior would not really work out in terms of a prolonged campaign. It would get really old. It's okay when it's in small doses and when it's actually with the approval of the GM and of the group.