This is ofcourse, the most important part of roleplaying. I mean, maybe you have read the Lord of the Rings and you really liked the character of Gandalf. You might want to call your roleplaying character Gandalf, make him look, talk and think like Gandalf and make him have the same powers as Gandalf. Well, so may four-hundred-and-seventy-three thousand three-hundred-and-thirty-six other people out there.
Much better would be, if you took some of the aspects of Gandalf's character that you like, and put them together with parts from other characters and things you came up with yourself.
I know a lot of people who just copied a character from a fantasy-series and are very happy playing them. But usually those people added some other aspects to those characters, or they took a character that is very complicated.
Also, a lot of roleplay areas leave the storyline to the players. They should come up with the quests and stuff like that. In those cases do not be afraid to add a fragment of your own. As long as it is realistic within that world, it is probably appreciated. With all these things there's just one main idea from my point of view:
Whenever something is original, it is good.