Anyone who has spent a lot of time in the world of fan fiction knows about the danger of Mary Sues - characters that are obviously the author writing a perfect version of themselves into the story. It is possible to create an original character that's not a Mary Sue, however. Here are some of the things I try and keep in mind when I create a new character. (Some of this information also applies to writing any character - original or otherwise)
No person is perfect. One good step in making a character believable is giving them some human flaws.
People change over time. A character should not be stagnant, but rather shaped by their experiences.
People have pasts. Unless your character is an infant or an amnesiac, their past experiences constantly influence who they become and their everyday actions. This is not to say create a great tragedy in the past of your character. This is simply a reminder that characters have parents, siblings, educations, childhood friends, etc.
People have strengths and weaknesses. Just as some people are better at some things than others, they also have to not be as good at other things. No one excels at everything.
Not everyone can have super powers or be a Slayer, a vampire, a werewolf, a witch, etc. Some people have to be...well, normal.
Relationships evolve over time. One of the most common signs of the "Mary Sue" is that they are suddenly involved in a relationship with a major character. You can keep this in mind for unconventional relationships and even friendship situations as well.
Not everyone is drop dead gorgeous. As much as we might like to be, we can't all be super models.
There is a tendency, when trying to avoid creating a Mary Sue, to also avoid anything from your own life in the character. This can result in characters you care (as a reader or a writer) very little about. Consider adding elements – motivations, emotions, personality quirks – from your own life to give the character depth and to make them interest the reader. A character who can be identified with is far more interesting than one you have nothing in common with.
Mary Sue Page