I always found it really hard to have real moral choices in games. If the game is self contained, the player is usually encouraged to just play to win although the game can try to give you a bad conscience for a certain choice (like you may get a benefit if you are willing to eat children etc.).
I appreciate when games attempt to do this. Its great for many reasons, 1) usually the gameplay and decisions are more difficult 2) it makes your decisions carry more weight thus more meaning 3) more meaningful experiences 4) can make people think about what they are doing and hopefully have a positive impact on them.
Freedom: The Underground Railroad did this to some extent with the decision points around the slaves you free versus the ones you let get captured. It really sucks when you have to sacrifice for the greater good. But in the end those decisions meant something.
I think there is room to experiment with horror games as well. Not just zombie games but games were terrible things are going to happen you can impact those things.
The first thing that I can think of is Legend 10 (=Scenario 10) in Legends of Andor (or rather its first big expansion), a coop where the players have to decide which of the two sides in a battle to support. Supporting the attackers gives you access to more powerful weapons for the final battle, but even though it would have been interesting to explore this aspect of the game (you also get to read different story cards), I could never yet bring myself to letting our group join the aggressors. While these are definitely not represented as purely 'evil' in the game, the fact that they were willing to attack and kill former allies always meant that I didn't want to support them, even if it would make winning the game somewhat easier. And even though it's 'just a game'.
Possibly these moral choices get even harder in a competitive game? In a coop, the moral decision is always for the whole group, and you win and lose together, whereas in a competitive game, someone always wins.
C&H Schmidt - competition tends to serve as a justification for behaving in a less moral way, you can always say something like "well somebody has to win". I think that the best way to include morality in a game is without any special mechanisms or karma systems, I lean toward introducing the meaningful choices through the story - like in a good role-playing session. How many times have you heard somebody say "OK, lets kill this guy, he's in our way" - why is it so easy? Because "this guy" is just a piece of cardboard with a picture, there is no story behind him. You might like him more or less, due to the graphical representation, but you don't feel connected. Whereas if the characters in a game's world are like you or your friends, they feel and live it is not as easy to send them to the other side... at least it shouldn't be. Now don't get me wrong I love me some hack'n'slash from time to time but I kind of feel I want something more, something more meaningful, a feeling similar to the one you have after reading a good book or watching a brilliant movie.