Player characters come in all forms. There's the classic goodie two-shoes hero, the damaged anti-hero, the blank slate, etc. For me, the most interesting aspect in games, and adventure games in particular, is the character development. In a good game, your main character won't be the same person he or she was when they began their journey. Still, the choices they make and the actions they perform define them, and sometimes, if something comes out of left field, it can ruin immersion as well as believability.
Starting off a game with a new main character is always an interesting challenge. How much of the character's history do you reveal straight away? Is there an air of mystery about them you want to preserve? Will the player find it difficult to sympathize or put themselves in the role if they don't know everything about them?
Once you do get to the point where the player "knows" the character, it gives you some room to play around. However, you must be conscious of what you've already established. It will seem very out of place if a character who has been shown to be respectful of the law begins committing crimes out of the blue. It all depends on the context of the story, really.
What happens, though, if your story is about someone who starts off good, but goes on a downward spiral into evil?
I have to confess I'm not a huge fan of Star Wars, and only recently saw all 6 movies (gasp!) Although I'd heard little good said about the prequel trilogy, the aspect that interested me most about them was how they showed Anakin Skywalker's gradual corruption and transformation into Darth Vader. Unfortunately, this wasn't handled very well, and it seemed rather abrupt, which is an easy pitfall.
If you have a protagonist who is going to go over to the non-righteous side, how far is too far? If you want to show them becoming a completely unlikeable ass, then the sky is the limit. If, however, you want your audience to feel sympathy, or even give them a shot at redemption, you have to be more careful.
It's a dilemma I'm currently struggling with, but I think I have a general idea of what the limits are.