I agree with KRyan that D&D would be better served if alignment were thrown out wholesale.
However, I don't think that treating Good and Evil as arbitrary labels if you keep them in (like subtypes) is the best idea -- first and foremost, because we have subtypes, and that's literally what they do. Replacing the axes with another such as the BRACI grid might serve you, but my suggestion is to interpret the two dichotomies however appropriate. You're never going to find a rigid nine-state grid system that properly accommodates all characters. I mean, what morality grid can you possibly imagine that can simplify all of sapient morality into nine opinions?
Therefore, in order to avoid the task of dealing with what I'll have to do to the other game rules if I throw out alignment, me and my group have a collective, broadened understanding of the current alignment grid. This interpretation hasn't been written down anywhere until now, so I'll try to do my best to explain.
On the good/evil axis, neutral is far and away the most common alignment.
After careful consideration, it became apparent to us that nearly everyone except adventurers (and, judging by the amount of murder-hoboing, even most adventurers) would be Neutral along at least the good/evil axis. Most people simply worry about their next harvest (or paycheck if you're not doing a fantasy setting). They have too little to give and can't find it in themselves to ruin others' lives in order to better their situation. More importantly, most people aren't ambitious, which drives both good and evil attitudes (it takes some serious balls to want to join the peace corps, after all).
"Law" vs. Chaos would be more adequately named "Order" vs. Chaos.
We aren't pedantic about semantics, but I couldn't find a better way to sum that up in a bolded summary.
As it stands in our group, "lawful" or whatever you want to call it only describes your willingness to adhere to a defined set of beliefs or rules. I did not personally see that much of a problem with the Law vs. Chaos dichotomy until I saw both lawful barbarians and chaotic monks in other media (Diablo and Legend of Korra, respectively).
Of course this spawns the classic problem of "what do you do with someone who is dedicated to Chaos conceptually?" This interpretation is made vague intentionally to allow the players and GM to come up with classifications on an individual basis. Most of the time, I think of "Chaos" as "lack of a governing body or set of rules," not "physical/magical entropy" or some other incredibly abstract phenomenon, primarily because it's ridiculous for even demons to believe that replacing everything with pure entropy would somehow better their situation.
On the flip side, Lawful Evil isn't as cut-and-dried in our interpretation. Generally what I've seen is that players tend to think any dictator or iron-fisted ruler is Lawful Evil. This is often not the case. For example, Joseph Stalin rarely followed any of the rules that he set for himself and others to follow. He also did not have any higher calling or authority (that we know of) to answer to, or any strict set of principles that he adhered to. In fact, he broke quite a number of laws to acquire his seat in the first place. A Lawful Evil ruler would transform the nation he or she took control of over a period of time so as to keep the population complacent and keep from breaking any laws while also suiting their needs at the same time. Revolution isn't out of the question, but the new ruler in question, having a set of principles, would at least follow their own rules that they put in place. That's just the way I look at it.
The monks I mentioned earlier are a pretty good example; they're quite obviously very high-level Monks dedicated to an order called the Red Lotus. Problem is, the Red Lotus is dedicated to unseating the Avatar (who maintains balance between the material and the spirit), and sees her as a tyrant or obstacle rather than a benevolent ruler. Their end goal is to make the world less orderly, but they're clearly disciplined and adhere to their tenants. What does that make them? Simple -- they're Chaotic Neutral, or even Good, because they're working to better the world and even offer the Avatar a chance to join them in a one-on-one parlay. Which brings me to the next point.
Ends don't justify the means for Good guys, but they do for everyone else.
Before I begin on this, let me clarify that I'm using the very basic definitions for Good and Evil; Good is bettering others even if it harms yourself, and Evil is the opposite.
This is a theme that pops up constantly in "good vs. evil" themed campaigns and adventures that want to give the players a serious moral choice or consequence. I've seen it come up countless times in personal and recounted experiences. In other words, if you're willing to kill 49% of people to save the other 51%, then you've settled for less, and you're not Good. The key part to being Good is the empathy.
The reason that the axes are asymmetrical here is because it's harder to be Good than not. Actually trying to be Good is detrimental towards being the player character while being Evil isn't (at least, in the short-term), by definition. Minimizing losses is not Good, neither is benefiting others when it's convenient. However, the ever-tempting option of "Kill your employer and take the macguffin AND the money" always exists.
There's a joke I've heard that Lawful Good is the easiest to play when you're new to roleplaying, then the hardest to play once you've understood the game. This is mostly true; for new players, the restrictive conduct required out of a Paladin gives them cues and motivation to do things in-character that they might be lacking otherwise. But for one whose mind has been opened up to the possibilities in a given setting, Lawful Good is more of a hindrance specifically because you must follow those rules. Evil does require some finesse too, since it easy to commit a string of violent acts but hard to make your string of violent acts memorable. Subtler evil machinations involving guile get high-risk fast and require some creativity. Playing a non-Neutral alignment is a difficulty step up for roleplaying.