Do characters who are 'half-breeds' annoy you?

[Silly Cat Alice Suspended]

Do characters who are 'half-breeds' annoy you? Not the character themselves, more like the concept that they are half this and half that. Or are you fine with them as long as the writer explains how it could happen?

And no, I'm not talking about half human half vampire, I'm thinking more like a half human and half angel. I'm *NOT* writing a story that deals with a half breed though. So please, state your opinions.