Today I took a look at a RPG messageboard and was immediately drawn to a thread entitled "So I finally have one of "those" players". "Those" players could mean a lot of different things in the RPG world: Players who are uncooperative or start fights regularly with other players, players who are "rules lawyers", players who insist on playing a certain character race or class every time... But in this instance the original poster was referring to a player who wanted to play a character that didn't seem like a good fit for the campaign setting and tone.
What do I mean by "not a good fit"? Suppose you have a player who wants to play a gnome. But in your campaign setting gnomes live deep beneath the earth and never visit the surface. All sorts of rumors and stories have grown up around them because no one has ever seen one in living memory, and most people think that gnomes are some kind of horrible monster. Or perhaps you have a player who wants to play an elf in a world where elves just don't exist.
I can empathize with the desire to play something that doesn't quite fit. There's a certain appeal to playing a character who stands out, who is unique. After playing roleplaying games for nearly two decades, I've played nearly every class and most of the races in traditional fantasy games, and sometimes the standard stuff just doesn't seem very inspiring..
Sometimes the awkward fit is a minor issue; one of my friends wanted to play a pacifist cleric in one campaign. That was a little bit of a challenge for the GM and other players because clerics are often useful combatants and everyone had to adjust to the idea that the cleric wasn't going to attack the monsters. But we managed.
A bigger challenge is when a player wants to play something that just doesn't exist in the game setting. In the same campaign as above, I wanted to play a race that doesn't exist in the game setting. The GM allowed it because the race I wanted to play was essentially human and didn't have any game-unbalancing abilities or physical traits that would be difficult to explain.
Many of the respondents in the messageboard thread felt the player was just being problematic, in part because the original poster explained that this player had done some problematic things in other campaigns. But even if the player sometimes did things that the other players didn't like, that doesn't mean he's a problem player. He probably wasn't trying to cause trouble by wanting to play a character that didn't fit in the game setting; he was just trying to play a character that he thought would be fun.
I know that's what I'm doing when I want to play something unusual. I get an idea, or more often get inspired by a tv show or book, and I want to try it out. I tend to think more about the good of the game than the player in the post apparently did, so I often relinquish my unusual character concept in favor of something that will fit more smoothly with the other characters and setting. I once had an idea for a character in a superhero campaign who had amnesia and didn't know anything at all about his past or how he acquired his powers. I imagined that perhaps some secret government agency would pursue him, either because he was an escaped test subject or because they, too, wanted to know about his past. But the GM I played superhero games with at the time probably wouldn't have done much with a character history like that. He tended to like very traditional four-color superheroes. I would ultimately have felt that I wasn't really getting to play the character I wanted to play. Plus, my story might have overshadowed some of the other players, and I didn't want that. In the long run it might also have turned out to be less fun than I thought to play a character with no history.
That's often my downfall when I think of an "inappropriate" character. They're usually too complicated to play, or too difficult to model in the game system we're using. In one campaign I started out playing a bard, then decided I wished I'd chosen to play a wizard instead. My GM kindly allowed me to take some wizard levels to satisfy my desire. But after I'd played that combination for a while I realized that it just made the character harder to play and didn't really give me what I wanted. So we retroactively removed her wizard levels, and the GM used a little GM fiat to allow her to keep some special abilities she'd acquired as the result of her wizard levels.
I'm lucky that the GMs I play with aren't of the "I'm the GM and I say you can't play that!" attitude espoused by some of the folks on the messageboard. My GMs try to make their players happy, because that means we're all having fun. They're willing to work with almost any character concept, although they might draw the line at a half-dragon, half-infernal, half-drow paladin/wizard who was raised by gnomes.
I wonder how you could make one of those work?