For me, there are three kinds of character:
1-The one who changes (Let's call him the Hero): A character is shown having a flaw which he has to overcome after great difficulties and reluctance. Paul Newman in The Veredict is a great example.
2-The one who can't change (The Tragic characters). A character whose own personality doesn't let him change, no matter how hard he tries or how much he know he has to change. There are plenty, but let's say Kane in Citizen Kane.
3-The one that doesn't really need to change: James Bond, Indiana Jones, etc. There's a second variety to this, in which the character needs to change but doesn't do it because he doesn't realize his flaws, although everyone does: Don Quixote and his derivates.
Perhaps there are even more. I know what there isn't. What there isn't is only one type of central character. Thank goodness. There in lies the grey area, the fun, the craft, the intrigue.