One of my favorite examples of this was playing The Legend of Zelda: Four Swords Adventure on the Gamecube back in they day. Me and a friend were really into it, but had trouble rounding up extra players. We got his little sister and an unwilling third friend to join. After about 30 minutes the unwilling friend, Marcus, gets bored with the game and starts sabotaging the rest of us. He'd run around smacking us with his sword making us drop rupees or refuse to stand where we needed him. That's honestly when it became fun for all of us, though.

The other three of us would plan out the room and then we'd figure out how to wrangle Marcus back into place. Someone would hold him so he couldn't go rogue and hit us while the others got in place to pull some levers before the wrangler would toss Marcus onto a pressure plate or something. He got to continue being a little bastard while we (slowly) made progress through the game. He eventually came around and helped us when it was absolutely necessary, but it was always clear it was just so he could keep being a bastard again. I really enjoy that asymmetrical style of gameplay and wish more things capitalized on it.

Also on the Gamecube of notable mention was Final Fantasy Crystal Chronicles. Always fun when someone would get the personal mission of "take the most damage" and become a suicidal maniac in every encounter, much to everyone else's detriment. Ah the good old days.