Recent example was a "standard orphan son" of Martin who was built using standard powers and guides. This young prince very quickly turned out to not fit the group in play or the culture of Amber (despite growing up there.) Some of this was Player generated (or lack of experience with roleplay), some was wrapped up in the motivations the character held dear. As play progressed, the Character (or Player) chose to make an issue of the fact that "royals" were stuck-up elitist wankers and that He was regarded as "common clay" and a putz. Basically, this was potential roleplay material, but the group could not make it work. The majority of the group just didn't buy into the confusion and attitudes sown by the young prince-who-acted-like-a-putz. Why did he do it? I think it was a mistake. The Player did not take an in-game "critical social dynamic" into account. The Family looking down on his Character did not appeal to him, nor did the manner and mistakes of his Character appeal to the other Family members. When in-game responses started to chastize his Character, the Player wondered why folks were "ganging up" on his prince. When Players out-game tried to explain that his Character was causing grief for the King and Family, he reacted as if that was his Character's business and no one else's. The Player left the game over this and other issues.
In another game, I had a Player choose to play a mute loner; very "non-standard." That lasted one session. It just didn't work. A case where invention was not justified or pragmatic to play. Yet, I've had a Player develop a background where their Character eventually discovered that they (and their sister) were of full dragon blood, born of a dragon in human form. They grew up human, and played out human, only learning slowly of dragon heritage as things went along. It never impacted the group dynamic, though it generated a lot of plot. There were no "groans" or "power gaming" issues at all. In fact, other players felt sorry for the Character as his dragon nature developed in fits and starts of odd, comic, and awkward moments.