Law, Neutrality, and Chaos represent a character's ultimate goals. A Lawful character seeks to create and/or solidify order in a given group or society. A Chaotic character seeks to dissolve any existing order, and prevent further order from forming. A Neutral character either seeks a balance between the two, or doesn't care too strongly one way or the other.
Good, Neutrality, and Evil represent a character's reason for seeking their goals. A Good character wants to give life, liberty, and happiness to as many creatures as possible, and is altruistic. An Evil character wants to deprive creatures of the same, and might be described as power-seeking. A Neutral character wants what's best for themselves, and might include others in their goals or not.
Lawful Good: Order for the sake of security and fairness. The Paragon.
Lawful Evil: Order for the sake of personal power and control. The Machiavel.
Lawful Neutral: Order for order's sake. The Bureaucrat.
Neutral Good: Balance (or status-quo) for the sake of tranquility and contentment. The Peacekeeper.
Neutral Evil: Balance (or status-quo) for the sake of maintaining personal power and control. The Tyrant.
True Neutral: Balance (or status-quo) for its own sake, or for some mystic reason. The Independent (or The Druid).
Chaotic Good: Disorder for the sake of liberty and happiness. The Dionysian.
Chaotic Evil: Disorder for the sake of personal power. The Destroyer.
Chaotic Neutral: Disorder for disorder's sake. The Wildcard.
Some examples from fiction:
- Randall Flagg in The Stand is a good example of Lawful Evil. He establishes a draconian regime that militarizes against Mother Abigail's "Boulder Free Zone" (based on the events in the miniseries, I'd call them Neutral Good for the most part). His methods are extreme, but they get results, and he's able to attract a large group of people that would probably be Lawful Neutral under a more benevolent leader.
- By contrast, Flagg in The Eyes of the Dragon is Chaotic Evil. He is explicitly stated as seeking to cause chaos and bloodshed, somehow feeding off of it. Note that his methods are not necessarily crazed or random, as many tend to think of Chaotic Evil; he plans methodically, playing a long game in the hope of creating utter, violent anarchy when his machinations come to a head.
- The priests of the Temple of Syrinx (from Rush's suite 2112) might be Neutral Evil; they do want to maintain their power, and head up a hierarchy to do so, but they don't really need to create further order as they already control everything. Their destruction of the guitar seems to be motivated more by spite than by a desire to maintain the hierarchy; otherwise, their behavior might occupy a grey area between Lawful Neutral and Neutral Evil.
- The Vogons from The Hitchhiker's Guide to the Galaxy are extreme Lawful Neutral. Few of them seem to enjoy causing death and destruction, but they aren't bothered by it so long as it's done according to the proper procedures. Their destruction of the Earth is amoral, yes, but not malicious; Jeltz mutters "...apathetic bloody planet, I've no sympathy at all." This seems to imply that they would have happily left the humans alone if they had bothered to get down to the planning office and register a formal complaint; the hierarchy is paramount. (Side note: I wonder how strongly the Modrons were influenced by the Vogons...)