For those unfamiliar with the 1e AD&D formulation of the now-classic 9 alignment system, here's a gloss on the general idea. (It's not everyone's interpretation, but it gets to the point.) In the Player's Handbook, alignment is presented largely as a worldview of characters in a way that might be familiar, but in the Dungeon Master's Guide the mask is torn off. Alignment isn't just philosophy, it's something much more like an "army list" from a war game. (Indeed, in the war games that gave birth to D&D, alignment really was an army list.) In the section on Changing Alignment, on p. 25 of the DMG, Gygax tells the reader that:
Whether or not the character actively professes some deity, he or she will have an alignment and serve one or more deities of this general alignment indirectly and unbeknownst to the character.The same section goes on to imply that character level is a sign of favour from the character's extra-planar patrons, easily revoked from those who break faith. Similarly, the explanations of the alignments differ, making it clear (for example) that those who merely act out a worldview inclined towards randomness are in fact serving Chaotic Neutral, a supernatural alliance that seeks to eradicate life itself.
Over time, the Dungeon Master's Guide interpretation of alignment as allegiance has vanished. While connections to the Outer Planes are still drawn at times, it's far more common to see emphasis put on the character's personality as demonstrated by their actions. Lawful characters are disciplined, Chaotic characters are free spirits, and so forth. Similarly, level is seen as a function of the character's own prowess, independent of any patronage.
Let me pause here to draw out the primary distinction with an example. (Lest anyone consider arguing the toss here, I'm looking to sketch on paper to get my thinking across, not set definitions in stone for all to use.) Imagine a vicious psychopath with no care for anyone else in the world. While a truly cruel person, the protagonist of this story is also terribly fearful of divine retribution in the afterlife. As a result, the protagonist has chosen a life in the service of a generally admired church whose works serve to strengthen civilisation, ease the suffering of the meek, and check potential abuses by the strong. This church has occasional call for killers, and there our protagonist has found a calling for their sadistic tendencies. Under a planar-based alignment system, the protagonist is somewhere in the zone around Lawful Good by acting to further the cause of the corresponding Planes. If one is using a personality-based alignment system, it's not really clear but I think that Lawful Evil (self-centered but obedient to lawful authority that protects their interests) would be a fair way to represent the type.
Note that uncertainty at the end of the example. I could understand someone saying that the protagonist is Neutral Evil, or Lawful Neutral, or perhaps even Unaligned Neutral, Lawful Good, or Chaotic Evil. (The Chaotic and Good corner of the alignment grid I think is ruled out, but perhaps I'm just being a stick in the mud?) D&D still has the Player's Handbook version of alignment-as-worldview and many of the rules that grew out of the alignment-as-allegiance of the 1e DMG, but it's empty of content without the deeper explanation. This leaves players of the game to trade opinions about "what a good person would do," while the game mechanics imply that matters of good and evil are objective features of the world. Some players are so frustrated that they declare alignment a dead letter, and many of this group go on to propose that alignment-based magic be geared around the alliances of patron deities. That natural turn suggests to me that the fundamental, forgotten idea of alignment as allegiance to supernatural powers is sound.
Of course, there's an objection that using the planes only moves the problem one step away and that my interpretation just leaves us to argue about "what a good plane might do". I tend to think that this is a problem of language rather than morality. Treat the alignments as proper nouns. No matter whether one views their actions as all that lawful or good, the Seven Heavens just are Lawful Good - and they have the Holy Words to back it up. The DM has a duty to be consistent in conceiving the aims of the planes (just as she has a duty to represent any NPC consistently), but the players ought to be as uncertain as their characters.
I should also take up for restoring some of the alignments that have fallen by the wayside. It's fairly well-known that True Neutral in the old sense of balancing off the Outer Planes is basically gone and replaced first with an attempt to balance one's individual conduct (lampooned as "I was Lawful Good yesterday, I'd better be Chaotic Evil today), then with an "unaligned" category with just a tip of the hat to valuing balance. I put it that if the idea of the other 8 alignments anchored on the Outer Planes is appealing, the players deserve a "None of the Above" option that puts the Prime Material Plane first.
The other great change to alignments came about when the default human alignment moved from Lawful (as city- and nation-building folk) with some inclination towards Good into the new Neutral ("just act naturally") category. It strikes me that this change has not necessarily been for the better. Firstly, if humans are "natural", then one has to find a way to out-Lawful them in order to be Lawful - not the easiest thing. Secondly, the Chaotic alignments dropped off the far edge so that Chaotic Neutral is just individualism rather than all-consuming Entropy. This led to Evil having to pick up the slack and incorporate a lot of destruction, rather than just being self-centered. Strikingly, a recent Pathfinder RPG supplement offers up the "Annihilist" as a type of Neutral Evil, explaining this world view as an acceptance that,
"Nothing matters. Entropy and chaos have created a world where nothing lasts, nothing means anything, and even the greatest works or truths will fall to dust and obscurity in the blink of an eye.... [You see] entropy and death everywhere, and accept (and inflict) them as the true pillars of reality." (sourced from the Pathfinder SRD)
This is all well and good, but it's meant to be a philosophy within a greater creed of those that "embody pure selfishness". I suppose it's possible to be selfish and think that nothing matters, but I can't help but see this as Evil doing too much work. Not every threat to the world needs to come from Big Bad Evil Guys - let Big Bad Entropy Girls in on the action!
That point leads in to a quick note on the much-beloved "special case" of the alignment system, the Paladin. Using the planes to anchor the system tells us what is going on with members of this class: they're uniquely empowered by Lawful Good to carry out an uncompromising struggle against the servants of the Evil planes. Any willful deed that furthers the cause of Evil is utterly unacceptable, while aid to Chaos is an abhorrent but forgivable transgression.
For a long time, DMs and players have clashed over the difficulty of Paladins faced by a choice between killing an innocent and allowing Evil to gain some great advantage. The last treatment I read on this was Duane VanderPol's firey article in &13, in which DMs were blamed for stirring trouble. I still have some sympathy for Mr. VanderPol's outlook, but I think his strategy might be wrong. Recall, for a moment, that Chaos is an entropic force that seeks to destroy the world. Evil just wants to put the meek at the mercy of the strong. That's the stakes, and the problem, for players wanting to play a Paladin. DMs can forget moral quandaries about killing innocents and such - at worst, that's offering weak assistance to Chaos and the Paladin is permitted to do such things under duress. Start sticking Paladins with the choice between Chaos and Evil! Suppose there's a powerful Chaotic threat that is about to overwhelm a Lawful Evil presence, with Lawful Good folk next in line. The Paladin certainly shouldn't ride to help agents of Evil, but other characters might note that the Chaotics would be more easily fought with other Lawful folk as allies...