There seems to be a great disparity among players as to the exact deffinitions of each alignment. In addition, while the Player's Handbook might state one iron-clad deffinition of True Neutral, for example, there are other deffinitions. Some players do not easily fit into the predetermined molds that Dungeons and Dragons tends to impose. Because of this, the following dissertation on each alignment has become necessary -- not only to give veteran players a better scope of alignments, but also to give newer players a better understanding just what alignment is.
Alignments, in general, are world-views. The classic examples are Good and Evil, but there are always varying degrees of Good and Evil, Right and Wrong. Dungeons and Dragons breaks this down further into Good, Evil, Neutral, as well as Lawful and Chaotic. Good aims to make the world a better place, Evil aims to either destroy or corrupt, and Neutral chooses its battles, sometimes on one side and sometimes on the other. Lawful alignments tend to follow certain rules, be they national, political, religious, or personal codes. Chaotic alignments tend to be unpredictable, doing as they please from moment to moment. Displayed below is are two crude breakdowns of the alignments into the classical nine 'true alignments', color-coded by either Nature, or Code.
Because of this breakdown, we can also see which of these alignments are in opposition to one another. For instance, Chaotic Evil's antithesis is Lawful Good -- and Chaotic Evil personalities tend to clash with the full spectrum of Lawful codes and Good natures (as shown below), because of the classic Good vs Evil theme, and the Law vs Chaos themes.
This opposition rule works well for the four corner alignments: Chaotic Evil, Lawful Good, Chaotic Evil, and Lawful Evil. In the cases of the four cardinal alignments (Chaotic Neutral, Neutral Good, Lawful Neutral, and Neutral Evil), we tend to see a slightly different breakdown of oppositions (as shown below). Neutral Good, for instance, is in direct opposition to all Evil natures.
These opposition studies are important when considering the alignments as a whole. Nations in opposition to one another cannot know peace. Races in opposition to one another know only war. Characters in opposition to one another within the party rarely survive the night.
Alignments as a whole, however, are a matter of personal taste when a player creates a character. It's also a matter of designing a character compatible with that alignment. Good. Bad. Unpredictable. Stoic. Most world-views, or alignments, can be fit into these nine categories. The nine categories are not inflexible, and there are a number of subalignments within each of the primary nine alignments.
It's important to remember that 'lawful' tends to mean a character is predictable in some fashion. Lawful characters tend to follow some sort of code, be it the law of the land, or a personal ethos. Admittedly, some 'lawful' characters only pay lip service to the law, such as the mob or corrupt politicians. Chaotic characters tend to be more unpredictable. They may follow a limited code of sorts, but it tends to be a malleable code, open to interpretation and experience. Chaotic characters do not necessarily sew chaos wherever they go; they just tend to be chaotic, themselves.
Quite the contrary. While there are 'lawful stupid' Lawful Good characters, there are alternatives. Lawful Good can exemplify a soulful samurai, a world-wise paladin, or just a regular guard who believes in what he stands for. Most good-aligned nations are actually Lawful Good, such as King Arthur's Camelot, or the modern-day United States.
Lawful Neutral personalities tend to follow the letter of the law, rather than the spirit of the law. Because of this, beauracracies often fall into this category. Many Lawful Good societies sometimes degenerate to this, rather than idealizing the original intentions. Lawful Evil societies can also be inhibited by the beauracracy, so it is not necessarily a 'bad' thing.
Monks seeking personal, spiritual enlightment above all else, or individuals who consider themselves above Good and Evil can also fall into this category.
Some people believe in something beyond Good and Evil. Like Neutral Good, they may be either fanatical or lackadaisical, but the essence of the alignment is a belief in something other than Good or Evil.
Many, like certain druids, believe that there must be a balance between Good and Evil -- that without the balance, neither benefits, to the detriment of all. Some True Neutrals will change sides in the middle of a battle, in order to maintain a balance. Such people are considered 'low balancers', because they change sides so often. Other True Neutrals will change sides only in the long-term, or if titanic forces or involved -- they are known as 'high balancers'.
Another form of True Neutral -- and probably the most common -- is 'coin'. Many people will do anything for money -- Good and Evil mean nothing to them. They follow a personal code of their own, but it if the money dictates Law, then so be it. If the money dictates Chaos, then so be it. True Neutral alignments tend make the perfect assassins, as they follow their orders for whatever pay, no matter the situation.
Other Chaotic Neutrals are those that must sew chaos, and care not for either Good or Evil. Any kind of status quo is anathema to them, and they may follow the dictates or a given situation as their hearts desire.
Too many players use Chaotic Neutral alignments as an excuse to do whatever they want. These characters tend not to last long, however, as the Dungeon Master must do away with them.