The question of morality in games all too often ignores the issue of ethics and meta-ethics. In a lot of games, as ThrashJazzAssassin says, the role of ethics is taken up by game mechanics, where a moral decision is one that conforms to a particular binary choice (good/evil, Jedi/Sith, Paragon/Renegade etc.). Philosophers have been struggling since, well, forever, to determine where moral get their oomph. In games, the choices are often presented as good or bad as though the choice is a clear one or, in rare cases of ambiguity, where there is a definite right one. Perhaps a player has a strictly conseuentialist viewpoint (only the results of actions matter morally) or perhaps they're more about values and unbreakable rules. The point is that morals are complicated because ethics are complicated (because meta-ethics are compicated).
I think an ethically reflective system of morality in a game would be really interesting, where moral decisions don't chart how much like Satan you look or how white your clothes are, but instead where the moral choices you (or your character) makes inform your ethical position and your character's, well, character. For example, imagine how much more satisfying a payoff it would have been at the end of Bioshock if your moral choices weren't framed in terms of good or bad, but were framed in terms of your relationship to objectivism. There are so many in game references to this philosophical system, and at times the game does a good job of exploring them, but when it comes to the ultimate moral judgment you're either a power hungry asshole or a lovable old coot. I suggest that had the designers framed the moral choices in relation to an overarching ethical system, the result would have been a potentially more illuminating and satisfying game.
Without an acknowledgment of the complexities of ethics and meta-ethics, which serve as the foundation for moral choices, games can only ever provide a moral system that rewards conformity to the developer's conception of ethics, an over-simplified and unsatisfying set of moral choices and/or a set of meaningless moral choices. Only when the game allows us to approach a moral question in reference to our own (or roleplaying self's own) ethics (derived from meta-ethics), and ideally responds to it, can moral questions be anything other than a gameplay mechanic.
Indeed, if games can provide a reflexive system that allows the player to really test and examine their own morality, the claim that games cannot be art since they require interaction is really turned on its head.