First, what is alignment? Well, actually, that's pretty much going to be the rub for the whole article. But, to begin with, alignment is a shorthand system used by many gaming systems to pigeonhole a character's moral outlook. The most famous system is that of D&D, which uses twin axes of Law vs. Chaos and Good vs. Evil. Other systems either use different alignments (e.g., Palladium's rather random collection), use a whole different kind of scale (e.g., WoD's Virtue/Vice mechanic paired with Humanity), or use descriptors rather than pre-defined alignments (e.g., FATE's Aspects, FantasyCraft's allegiances and paths). And, many systems just chuck the question out altogether, and assume you can describe your character's motivations without needing labels.
I find the labels to be handy, though. They are mostly handy for the reasons that labels are always handy. They get you 80% of the way to a mutual understanding with a single word or short phrase. However, like in life, we have to be careful to remember that labels are just shorthand. They are not "one size fits all," and they should not be used to automatically include or exclude anyone. That other 20% you need to reach true understanding is pretty damned important.
It's Just a Label
For me, the easiest way to understand alignments is to stop treating them as some sort of fundamental building block of a character's personality. Too many people use alignment as a driver and stricture for behavior. Instead, think of it as being equivalent to one's political party. Instead of Good and Evil, think Democrat and Republican (I am not making any statement about which party corresponds to which end of that axis). When you meet someone who self-identifies as a Democrat, you can make certain assumptions about their values. Of course, there are many different kinds of Democrats. So, let's also introduce the axis of Liberal vs. Conservative (to parallel the Law/Chaos axis). If you meet a Conservative Democrat, you can make a LOT of assumptions about the values at work. However, those assumptions are based on very broad generalizations and a general lumping together of value judgments that tend to correlate (even when there is no actual logical connection). That specific person may deviate radically from the party line on some particular issue.
As another example, let's look at the Houses at Hogwart's. Brave vs. clever vs. loyal vs. ambitious. All of those within a given house tend to share a number of traits, and a general outlook on life. However, they are not forced to follow the values of their House. And, each House clearly has members that differ significantly from the norm (e.g., Pettigrew, Diggory). Also, there are a number of students who could easily fit into multiple houses. Potter himself could easily have gone Slytherin. Hermione could have gone Ravenclaw. Just because you have a primary affinity to one of the Houses doesn't mean you outright reject the other three.
So, alignment is simply a general suggestion of values that tend to group together. Two "Lawful Good" characters can still radically disagree on any number of philosophical points, and especially disagree on the actions that should be taken because of them, without "violating" their alignment. A paladin can kill a baby, if doing so is either necessary to serve the greater good, or he honestly believes the baby is evil (e.g., the spawn of a devil). It is one of those hard choices, though, that will likely haunt the character. He may spend the rest of his life trying to figure out if he did do the right thing. Just because it did not cost him his divine power, does not mean that it has no consequences.
Who Among Us Is Truly Evil?
In what may be a radical suggestion, I think that one of the biggest problems with the D&D alignment system (other than the absolutely dreadful and categorically incorrect write-up in the 2e PHB) is that they use Good and Evil as one of the axes. The basic problem is that that effectively removes a third of the graph from consideration for PCs. No one wants to self-identify as Evil. And, no one wants to travel with someone who does so. It also introduces the Slytherin problem: Why do the rest of the upstanding members of society allow these people to exist? If I cast detect alignment on someone, and it comes back "evil," wouldn't I be justified in removing that person from the general population? (Yes, we can descend into thorny personal rights issues, and discussions of intent vs. action, but I think you understand my point.)
What if we re-labeled the axes just a bit. Not redefining them significantly, but just using words that do not create knee-jerk assumptions of one being "better" than the other. Instead of Law vs. Chaos, let's use Order vs. Chaos (most people think that being a law-abiding citizen is an inherently good thing). Instead of Good vs. Evil, let's use Altruistic vs. Egoistic. This still has something of a bias. But, simply putting oneself first is not automatically a bad thing. Also, as a note, each of these axes has a "Neutral" value in the middle, just as D&D does.
The advantage here is that you could now easily have a hero (well, probably more of an anti-hero) that falls well on the Egoistic side. Han Solo springs to mind. He would definitely fall in the Egoistic Chaos square, despite being a "good guy." Sure, most of your villains would also fall under Egoistic, because most people who put the needs of others first don't set out to conquer them. But, that's not necessarily true. It would not be hard to envision a well-meaning priest, who falls under Altruistic Order, instituting an oppressive religious state to try and stamp out sin and corruption.
This is Not the Stick You are Looking For
As a final point, alignment tends to not only be used as a straitjacket, but as a bludgeon. This is most obviously seen in the case of the paladin, in which the code of ethics is intended to be part of the class balance. But, it has been seen elsewhere (for a long time, there was a rule that if the character changed alignment, there should be an experience penalty). In my opinion, this is a crude solution to a problem that is largely caused by immaturity. Certain types of players, particularly younger ones and particularly ones that learned to play games on the computer, don't like dealing with ethical problems. They just want to kill things and take their stuff. Being evil makes that easier, so they go evil. And, because none of the people they hurt are real, they tend to go on sprees of destroying villages and murdering shopkeepers.
Whacking these players with an alignment stick is entirely the wrong response. For one thing, all it teaches them is that they should have picked an evil alignment to begin with, because clearly evil people get to do whatever they want. Instead, you need to look back to your Psych 101 course, and reinforcement techniques. Have NPCs treat the "good" characters with trust and respect. The "evil" characters get shunned, or even are branded as outlaws. Using in-setting consequences to influence actions is a whole post in itself. But, the point here is to have the reactions of the world shift to treat the character as the alignment he or she is portraying.
And, do not be afraid to shift the character's alignment to be in line with the actions he or she is taking. When it is a predictive label instead of a core belief, there is no reason not to say, "Yeah, I used to be a Democrat, but now that I've gotten older I find that the Republicans are saying more things I agree with." There is no need to punish the character (or the player) for this, especially if the character is being internally consistent otherwise. It is simply a case of the character either outgrowing the original label, or the labels just not properly covering the character's actual beliefs (an easy situation with only nine labels).
A Final Word
The one caveat to this, though, is that in the default D&D setting, alignment is a tangible force in the world. Law, chaos, good, and evil are as real and influential and earth, air, fire, and water. Changing your alignment changes how many magical effects work around you. The simplest solution to this, of course, is that most people do not come anywhere near the elemental poles of the four alignments. By the standards of the Outer Planes, nearly all humans are simply Neutral. This is reinforced somewhat in 3.x, as spells such as detect evil make a distinction between "little e" evil, like Enron, and "big E" Evil, like The Devil. Only people for whom their moral fiber is key to who they are, specifically priests, paladins, and the like, even register on the "big A" Alignment scale. Everyone else, on the "little a" scale, is just indicating which of the poles they lean towards. I think this rule works well (though it does make the plot of the corrupt bishop a bit difficult to pull off).
I'll just close with an interesting bit of wisdom I saw in an RPG.net signature (I forget whose): Remember, "good" people can kill things and take their stuff. But, if you either kill things and don't take their stuff, or take their stuff without killing them, then you're "evil."