One thing about Dungeons and Dragons that really appealed to me was the way it imposed a game structure-- a simplification, an ordering-- on life as a whole. It allowed me to think about philosophy, character, and story by making it simple enough to approach one piece at a time. Of course any simplification is a distortion; compression inevitably introduces artifacts. But the model is at worst merely wrong; without any model our ideas are "not even wrong." The D&D version of philosophy makes falsifiable predictions, so is useful as a starting point for thinking about these kinds of issues.
You see a lot of D&D type simplifying of the world in 1600-1900 European modernist philosophy. It's all binary oppositions and the imposition of an oversimplified order. Since their invention as a kind of small-scale wargame, tabletop roleplaying games have since moved in a more postmodern direction, emphasizing narrative and creativity, areas where they still hold the edge over digital RPGs.
(I am going to use all male examples below, but looking at the difference between how male and female characters in fiction realize these archetypes differently would itself be interesting.)
Lawful Good versus Chaotic Good: I think this is essentially a religious question. A rational atheist may believe that laws are useful for society as a whole, but at any point his decision to follow a particular law depends on the law's utility. He may recognize that following the law as a default behavior avoids having to make difficult moral computations that can be paralyzing, but if he thinks breaking a law will serve a higher good (even after weighing its effect on society), he will do so. A true anarchist can be chaotic good since he only wants everyone to be equal (an-archy). This is the Superman vs. Batman conflict.
Chaotic Neutral: This is Captain Jack Sparrow, or Coyote the trickster god. His goals are often selfish and he carelessly hurts others; but he is not actively seeking power. He doesn't actively oppress others. I think a lawful good character would judge that a chaotic neutral character, by not being lawful good, is in fact evil. Personally, I thought that the point of Pirates of the Caribbean was to make a comedy about alignment. You have lawful good characters who gradually become neutral or even chaotic good. There are also lawful evil characters, who are fairly rare in fiction, and a lot of the interpersonal conflict is driven by these differences in alignment.
Lawful evil versus chaotic evil: The lawful evil character is an authoritarian. He wants there to be an order, but he wants it to be his order. A lawful evil character is without mercy, but not without justice. I think of Javere the policeman from Les Miserables. The chaotic evil character is a monster, a predator. The Joker from The Dark Knight and Grendel fall into this category.
Lawful neutral: I think a realistically portrayed robot would necessarily be lawful neutral. For example, the terminator in the first film (despite its glowing red eyes and mean eyebrows) is actually lawful neutral. It appears evil to the characters in the film because the law it is following (its programming) pays no attention to morality, which for a person would in itself be evil (because part of our morality is innate and must be actively rejected.) But for the robot there is nothing but the law.
Here is a pretty good website, if you like this sort of thing:
All this also brings to mind one of my favorite comics: