Alignment

In many RPG systems, character alignment plays a central role in determining the temperament of the PCs that many of you will create. There are as many interpretations of the alignment system as there are GMs, and this article will detail my take on alignment, which is mostly in agreeance with the alignment videos produced by the GreatGM YouTube channel.
Personally, I believe that the ultimate goal of character creation is to come up with a person that is as complex and unique as the player creating them. Real people cannot be described in such simple terms as "Chaotic Neutral" or "Lawful Good," because their complex interests and beliefs will change how they react to certain scenarios. Therefore, a more complex understanding of the alignment chart is necessary to create someone that could be reasonably considered a realistic character, and as such, my personal take on alignment is described here. The description does not cover every combination of Lawful, Chaotic, Good, Evil, and Neutral, but discusses each of these five separately, and leaves the combined interpretation up to the player, who should ultimately decide who their character is, rather than allowing a chart to decide.

Lawful

Lawfulness, I find, is often taken to mean obedience to societal norms, or to some divine laws handed down by a godly benefactor, but this interpretation is problematic in a single, important way -- those laws are written by someone else, and are not specifically intended for the character that you create (in most cases). What does it mean to "follow the law" anyway? What if the laws conflict with each other? What if one divine commandment is that "thou shalt not kill," yet the lord to which you have sworn your service demands that you slay the local ooze infestation? Who's law do you break? Are you now chaotic?
This sort of paradox is the trouble you run into when creating a "lawful" character that only follows someone else's laws. Rather, a lawful character should follow a single, unified code which is personal to them and that they hold above all other law systems. Think of the archetypal vigilante superhero, the favorite example usually being Batman. While Batman does not go out of his way to break local laws or to frustrate law enforcement, he can and will do so any time those laws are obstacles to his own goals. For Batman, it is more important to catch the bad guy than to follow all of the rules of engagement laid out by Gotham City -- if his enemies don't play by the rules, why should he?
In a more fantasy-relevant setting, consider a paladin who is faced with the dilemma of either disobeying her god or breaking the local laws. Rather than being stuck in a bind, having a personal code has given her the necessary fallback to take decisive action without breaking character. She being a paladin, her personal code is probably heavily influenced by the guidance of her god -- maybe she even follows its commandments exactly. The important thing is that it is her choice to do so, she isn't just doing it because those are the laws, the player has actively decided that her character will follow the god's orders to the letter because that is the type of character she wants to create. 
We can extend this "code of honor" style thinking to characters who would normally be considered chaotic or evil by default. Now turn to the opposite of the example above and consider a dark paladin. In most traditional settings, a dark paladin is undoubtedly an evil and chaotic monster that eats babies and enslaves everyone she happens upon. Maybe this is true, but, we also tend to conflate chaos and evil. If the dark paladin practices her religion in the same was as the "light" paladin (that is, by following her god's commandments to the letter), then she too is lawful, regardless of the morality of her actions.
One must also remember that the code of laws to which you stick need not be noble and good! You will often find in pop culture that many "adventuring parties" have a lawful character who sticks to their principles no matter what, sometimes to the chagrin of the other members, and sometimes to their detriment! Consider the following two examples from Lord of the Rings: Samwise and Boromir. 
Samwise, I think, is a character who we can describe as what we would consider lawful good. His code is simple -- he made an oath to go with Frodo to Mt. Doom, and then destroy the Ring of Power. It is a simple code that is quite effectively utilized to create friction between Frodo and himself. So loyal is Sam to Frodo that he cannot bring himself to trust Gollum at any instant, which slowly drives a wedge between the two until he is finally asked to go home just before Frodo enters Shelob's lair. In this darkest moment, we see a Samwise on the brink of abandoning his oath (sort of -- it was Frodo's request that he leave, after all), but, being the lawful character he was, he resolved to rejoin Frodo and save him from Shelob against all odds. In this example, we see how a relatively simple code of honor can lead to such a powerful narrative that both entertains and moves.
Boromir, on the other hand, has a slightly different motive. His oath is to Gondor, his father, and his people. As a popular figure in the Gondorian army, he is constantly on the lookout for a way to give Gondor an edge in the fight against Sauron, which many would consider to be a noble goal. However, his dedication to Gondor has serious consequences as he tries to take the Ring of Power by force, and inadvertently assists in splitting up the adventuring party. Of course, he eventually realizes that by holding to his code of honor to Gondor, he has broken the oath he made to protect Frodo, and subsequently redeems himself, dying heroically. Does this slip up make him an evil man? Of course not, he never intended to bring about harm to Frodo or the group at large. While the Ring of Power did corrupt him, I believe that it only intensified the desire he already had to follow his code and give the Ring to his father. From his fall from grace, we can see that not every personal code has to be pristine and perfect, yielding only positive results, and that even a "lawful good" type of code can still create problems that can only be solved with a serious reevaluation of one's motivations.
To summarize, a "lawful" character needs only to follow a personal code they have laid out for themselves. This code can be morally right or wrong, legal or not, influenced by others or entirely made up, it doesn't matter. All that matters is that the code does govern their actions, at least in part. Similarly, the results of following the personal code, rigorously or not, need not always be exclusively positive, though beware of having an annoying law code that only forestalls the party's progress, or you may suddenly find a knife in your character's back. The most important rule of all is that whatever your code, make it fun to play with, that's the reason everyone is at the table to begin with.

Chaotic

To many, chaos is the opposite of order and lawfulness. I think that this is a reasonable definition, if you consider the two to be on a spectrum, with chaos on the one end and order on the other. Few people are totally chaotic -- we are heavily influenced from the moment of our birth by societal norms and values held by our family members. To be truly chaotic would be to entirely escape the lessons imposed on us from birth and to act entirely upon impulse and nothing else, causing us to be entirely unpredictable (to an extent). This definition in hand, I would assert that there is not a single person in existence who is perfectly chaotic with absolutely no sense of purpose and no code to follow. Someone who acts on impulse alone is nothing more than a mindless beast, incapable of using logic or deduction to reason about reality.
The task, then, during character design, is to figure out how chaotic your character can be without being a hindrance to the party. Always remember that being a dick because "that's just how my character is" is still being a dick. A reasonably chaotic character, I would say, still has a hint of lawfulness in him at least. There must be some underlying motivation that drives your character, even if it is as simple as "my character wants to have a good time." But, instead of adhering to a stringent code of honor or the like, a chaotic character primarily relies on his instincts to guide his actions, rather than taking the time to reason out a scenario and how it relates to his code.
Inevitably, in the discussion of chaos, someone will bring up the Joker as the perfect cinematic representation of chaos (usually people are referring to the Joker portrayed by Heath Ledger in The Dark Knight, which is the portrayal I will discuss, but with the introduction of Joaquin Phoenix's portrayal, some have begun gravitating towards his performance). The problem with this is that many people think that the reason he is the perfect portrayal of chaos is because he claims to be "an agent of chaos" in the film. While I would agree that he is on the far chaotic end of the spectrum, he still has an overarching plan, even if that plan is just to cause more chaos. The character wants you to think that there is no plan in motion and he wants you to think that he's just some crazy guy -- but the fact of the matter is that no one acting purely on instinct can plan the conversion of the "white knight" of Gotham to Two-Face. The chaos of Ledger's character instead stems from his lack of interest in the details of his plan. In this regard, he simply reacts instinctively -- by killing a mobster with a "magic trick" when threatened, or by letting Rachel fall once Batman asks him to "let her go."
Obviously, the Joker is an example of a "chaotic evil" character, but it is quite possible to take a similar approach to create a "chaotic good" character like Tiny Tina from the Borderlands franchise. While Tina is incredibly unpredictable by nature, her unwavering loyalty to her friends ensures that she will do anything to help them, usually with explosives.

Good and Evil

Neither good nor evil can be analyzed independently of one another. What is good and righteous to one man may be the bane of another. After all, it is said that no person is the villain in their own book. Rather than taking the traditional approach of labelling those who follow "radiant" or "light" gods as universally good, and those who follow "dark" or "abyssal" gods as universally evil, we should take a more subjective approach to the terminology. 
When wondering whether your character is "good" or "evil," the first question that should be asked is "relative to what or to whom?" Consider an archetypal necromancer, called Lena. Lena, by normal D&D rules, would be automatically a something-Evil alignment who probably summons skeletons to fight the party. However, in Ultor, Lena is basically a scientist, so labeling her automatically as evil doesn't really make a whole lot of sense, because there are tons of scientists that we are okay with, such as druids, arcanists, artificers, the list goes on. This doesn't mean that Lena can't be a bad person, but we shouldn't assume that she is just because of her profession. What we really want to know is "who's asking?" To a fellow necromancer, Lena is probably considered good, while to someone who considers necromancy an immoral art, she may be considered evil. 
It is complicated, then, to decide on what exactly your character is, and that's fine! People are complicated, and no person in history can be labelled a wholly good nor evil. It is no different in the worlds that we create. Goodness must be decided on a situation-by-situation basis, rather than in whole for an entire adventure. For this reason, I advocate that all alignment-restricted spells, classes, races, etc. have their alignment-restriction removed. Instead of forcing someone to be a particular alignment to cast a particular spell, merely consider the in-world consequences that casting such a spell would have. For instance, in Ultor, blood magic is illegal, but any player who wanted to could use it. If a player elects to use the blood magic, they don't automatically become evil, but how they are treated by those who know of this illegal act may change. Perhaps a bounty is placed on their head, or they are banned from certain cities, considered to be a menace. 
In conclusion, alignment should have no mechanical impact on the game in terms of what spells you can use or who you're allowed to worship. Alignment is merely a flavor mechanic that helps to determine how in-game interactions play out, and how that person is perceived by others, which can and should have a huge impact on gameplay. People are complicated, and reducing them to a binary good or evil doesn't make any sense for characters with any amount of complexity to them. In reality, your character will likely do both good and bad things, and the philosophical debate of whether the ends justify the means is endless and has no definitive answer. So when defining whether your character alignment is good or evil, you should choose a point of reference that is important to your character, because the other PCs and NPCs will all have varying opinions of you which depend upon their core beliefs.

Neutrality

Every scale has a balance point, whether the discussion revolves around good and evil or around lawfulness and chaos. In most traditional RPG alignment systems, this balance point is called "Neutral." Most people tend to be nearly Neutral, with only specific opinions being on the more extreme ends of either scale. Think of yourself, for instance. Are your views, or the views of those whom you know truly extreme? Most likely, they are not. Most likely, you hold the same views as most everyone else except for in a few specific instances, where you may feel more strongly one way or the other. We see this average neutrality in our modern political polls, where, more often than not, we find that our views align with "most people" who took the survey.
In a role-playing sense, Neutrality refers to the exact same thing, and merely describes where most of the population sits on the scale of lawfulness and chaos and on the scale of good or evil. There being two scales, there are two "Neutrals," both serving the same purpose. Again, there is no universal scale of what "Neutral" is -- good and evil are entirely subjective, and lawfulness is totally in respect to one-self, as described above. Therefore, "Neutral" for your character should be in reference to the things that most strongly define him/her. For example, being Neutral in regards to lawfulness means that while your character has a code, she won't feel especially compelled to follow it at all costs, if going against it seems to have more benefit. With respect to goodness, she will neither be a saint nor a particularly notable evil-doer. Her actions will mostly be passable to those who know her, but morally grey actions will not be out of consideration, should the need to take them arise.
This discussion brings us to the largest misconception that players have about the trait of neutrality, that being that if the character is neutral, then she necessarily doesn't really care about anything in particular, as she cannot be bothered to adhere to a code, either of morals or law. This belief is provably incorrect, as far as proofs about the human condition can go. To see why, let us consider the canonically "True Neutral" (Neutral/Neutral) character. By the standards of many systems and players, this character would be utterly devoid of any ability to care about anything -- not as a way of being malicious, but in the since that they literally lack the capacity to have opinions. Nonsense. There is not a single person that has ever existed in the history of humanity that has had absolutely no opinions on any matter in the world around him. By the false and stereotypical measure of True Neutral, your character could theoretically see someone murdered in front of their very eyes and feel nothing. They would not be afraid, nor disgusted, nor even consider the legality of such an action, they would simply observe the murder, and note it in their mind as something that happened.
Rather, a True Neutral character, were we to create one, would still have all the same opinions as any Lawful Good or Chaotic Evil character would have. Their neutrality comes not from their inability to care, but from their willingness to consider all sides of all spectra as equally valid, viewing both the overly lawful and overly chaotic as undesirable, and viewing the overly good to be just as pretentious as the supposedly evil. This does not mean that the character would not form a definite opinion on the events surrounding them, but that they would have no preconceptions that alter their decision in the end. Said in a more mathematical way -- if you took the sum of all of the character's actions with respect to the two aforementioned scales, they would come out to be exactly in the center of both, achieving "true" neutrality.
In reality, there are not really any True Neutral people in existence either. To be truly neutral is just as difficult to be truly chaotic -- you would have to totally escape all of the preconceptions and ideas placed upon you by those around you, and would have to approach everything in a truly logical sense before deciding the morality or legality of any action. It is possible, on the other hand, to achieve neutrality by making decisions that would be on "both" sides of the respective spectrum. For characters that you create, this type of neutral personality can be bland and uninteresting to play, as the character would simply have the opinions as mostly everyone else and wouldn't be too exceptional in their moral capacity. The better implementation is to allow your character to be neutral on most issues, but to choose a key few that your character feels especially strongly about, and to accentuate those opinions and use them for deepening your character's personality.