I usually make up the character but i do have a "type" when it comes to making my characters, it's more of a personality type, which is hard headed and sarcastic but kind, even if it's begrudgingly so. I alter the back story or more intimate details to suit the setting. Some times making her more bitter, or maybe more crazy. 

It seems like the only character I have set and always come back to is if it's an asylum RP.