To me there is a distinction between games which are immoral (or which have immorality) and games which are amoral. To me any game with a morality or reputation slider is by definition not amoral, as its judging your actions as either moral or immoral. No matter how much evil twisted stuff a game like this lets you do, its doing it while consciously allowing you to go against what it defines as moral activity.
Something like Prototype, which was mentioned earlier, comes a bit closer. The game doesn't give a crap whether slciing up infected, slaughtering marines, racing around the city or butchering innocents in nasty ways for jollies (though you don't get xp for the latter). But the spread of the virus means you'll probably spend less time butchering people as you go on, which means the average player's experience will roughly fit the protagonist's developing morality in the storyline. I think. It would be clearer if the game's cinematics weren't rubbish.
For me, Civ IV is an amoral game, and do not lets its bright look fool you. Civ IV's range of civics (defining features of your nation) can be mixed and matched however you wish, and are only seperated by their effects and how they are unlocked. If the game distinguished moral and immoral, it would stop you taking a "good" civic like free religion with a "bad" one like police state, but it doesn't care (the fantasy mod fall from heaven does distinguish good and evil, and stops you taking good/bad combos). Most experinced Civ IV players go with slavery not because they want to be EEEEEVVVVILLLLL but because its very powerful if min/maxed. If something else becomes better, they'll take that.
Similarly, Civ IV's AI nations aren't concerned with good behaviour so much as they are with their own interests. You can be a huge militaristic dictatorship and beat on a tiny pacificist nation and the only nations that care will be the one you attacked and its friends. An AI's interests are not always rational (some are obsessed with religion, some hoard technologies to the point of self destruction) but they stick to them regardless of what is usually considered right or wrong. Its not until the UN comes in at the late game that a moral aspect emerges, where the world can be forced to take "good" civics or ban nukes, but even that reuquires a vote, so it needs not to conflict with the interests of the majority. Note this doesn't mean Civ IV's designers are amoral, they are merely presenting a view of international relations driven by power and self interest as opposed to what is right and wrong, hence making Civ IV an "amoral" game.
EDIT: an advantage of being an english major is you usually have a dictionary at hand. From a note in the compact oxford english:
USAGE: immoral is not the same as amoral. While immoral means "not following accepted standards of morality" amoral means "without morals"