Personally, I don't mind students with special abilities or backgrounds, like veelas, vampires,etc. On the contrary, characters like that can make the RP a lot more fun, but only if they are intelligently developed, with a solid explaination as to why they are that way. Also, a bit of drama is always exciting, and since it's the wizarding world, pretty much everything goes.

However, there must be a limit. I'm annoyed when someone decides to change the canon HP storyline; they should adapt the character to it and not the other way around! Also, I have a huge problem with first years being madly in love or being able to do advanced magic from the moment they set foot in the castle. I think all actions should be age-appropriate, because otherwise, they make up the wrong kind of unrealism.