Chaosmancer
Legend
I used to allow anything. The a guy played seven foot tall albino elf who a pacifist who didn't have any weapons (not even sure he had a class). His character concept was that people were frightened of him, but gave no mechanical reason whatsoever. He lasted one game. Then when another guy wanted to play a half dragon half vampire I realized I had to start setting down some ground rules.
So before people join my campaign I send a link to some campaign ground rules and make sure everyone is on the same page. I have some racial and sub-class restrictions for thematic reasons.
In addition I have a a basic don't be evil or an antisocial emo loner who doesn't believe in working with anyone else because you want "room to grow" (but only if the other players read your mind and do exactly what you think they should). It's not that everybody has to be all rainbows and sunshine all the time, but some people think the entire campaign should revolve around their character. In other words, don't be a jerk and work with the group to come up with concepts that will work together.
So do I shoot down character concepts? I guess I do. I just let people know ahead of time.
Mildly funny story (it is funnier looking back)
The same group where I had the monk/druid ended up producing 4 characters who were anti-social and wore masks to hide their identities (one was a changeling so the mask was metaphorical).
About halfway through that game we were having a ton of table issues, players just getting angry and frustrated all the time. I pointed out that we had created a dynamic where everyone wanted to be alone and not support the other players, and that was the source of a lot of this conflict.
Everyone kind of just looked around and said "oh".
Things went a lot smoother after that realization and they started thinking a little more like a team.