D&D's alignment rules have caused a lot of confusion and angst in the past, and that's led to some (IMO) unfair criticism of the system. That's unfortunate; when I first encountered D&D, I thought alignment was one of the cleverer parts of the game.
Even within R&D, there's always been disagreement over how to define the axes of the alignment diagram. Some people want them to be broadly defined, others want narrow definitions. Some want the categories to be absolute, others want them to reflect local conditions. I've played with alignment in all sorts of configurations and concluded that it works best when the definitions are narrow and absolute.
In the beginning, D&D had a one-dimensional alignment scale, with Chaos at one end and Law at the other. This was a direct lift from the Elric and Corum stories by Michael Moorcock. In those, Law and Chaos aren't about legal rules or personal codes. They are the basic forces of the world, represented by opposing pantheons of gods. To say that you served Law meant that you aligned yourself with the gods of Law. You might or might not heed the local laws wherever you happened to be; that's a separate issue. Elric was concerned with Law and Chaos in the heavens because of the way those forces made their presence felt in the world.
Once Good and Evil were added to the mix in AD&D, the focus shifted substantially away from the gods to earthly concerns. Gods still had alignments, but they were more window dressing than raison d'etre. Alignments depicted attitudes and no longer reflected the foundation stones of the universe.
With that change, it became more important to define the alignments carefully. That never really happened. The definitions were left loose, with plenty of room for interpretation and waffling. Does Good mean you can't lie, or does that fall under Lawful? If I'm Chaotic, does that mean I go out of my way to defy local law, or that I place my own desires above those of others?
To clear this up, I propose the following definitions for the alignment axes. This approach was never officially adopted when put forward in the past. With current talk about bringing back two-pole alignment, it's important to have clear, narrow definitions such as these to relieve confusion and frustration.
The Good/Evil axis is solely about the value of life. Those at the Good end of the scale believe life has inherent value that should be protected and preserved whenever possible. Good characters aren't reluctant to kill when killing is necessary, but they never kill wantonly or cruelly. Good societies protect innocent life and have systems or traditions to alleviate suffering. Those at the Evil end of the scale believe life has no innate value or sanctity of its own; life is simply something that you have, or you don't have. Evil characters kill without remorse and have no qualms about killing innocents to achieve their own goals. Evil societies might engage in human sacrifice, execute minor criminals as a deterrent to petty crime, or treat murder as a lesser crime than theft. The Aztecs are a prime example of an Evil civilization on this scale, because of their massive institutionalization of human sacrifice.
The Law/Chaos axis is concerned solely with respect for social order, not with personal codes of conduct. Those at the Lawful end of the scale believe that everyone must work together for society to thrive and that coercion (law) is often necessary to make that happen. Lawful characters follow local laws (or customs where there is no written law) and expect others to do the same. A Lawful society has codified laws and the means to enforce them. The most Lawful societies extend the protection of the law to the very bottom of the social scale and its restrictions to the very top. Chaotic characters value individual freedom over communal good. They obey laws when it serves their purpose or insofar as they fear enforcement. Chaotic societies might be ruled by the changeable whims of their leaders or by whomever is strongest and most able to enforce their own wishes. If they have a legal code, it is largely ignored, corrupted, or bent in favor of the rich and powerful. The Roman Republic is a prime example of a Lawful civilization. Powerful patricians might bend it to their own purposes, but law was the oil that kept the great machine of Roman civilization turning.
Other interpretations are possible and equally useful. What's important is that the definitions are clear and narrow, as these are.