The first thing that comes to mind is whether your alignment is based around what you intent or what you achieve. If you got an evil demon pretending to be good to tag along with the party, they aren't going to get much of a chance to do much evil. However, does this make them good? They are doing good things, right? The general census among my players is no. Alignment pertains to your intent. If due to your 6 intelligence or pure bad luck you end up unintentionally unleashing evil upon the world, that doesn't make you chaotic evil. Willingly doing so because it sounded fun would. Probably.
Only having 9 different options makes alignments as originally described rather limiting. Typically I haven't seen them used this way. Some level of shading was always acknowledged in the groups I played with. You could be lawful neutral with a good bent. This will be obviously different from a character who is lawful good but hovering close to neutral. In our terminology having a bent was the same as hovering a bit closer to another alignment. Playing with the grades and shading between the hard divisions helps lead to more varied characters. It's also something that naturally happens if you go in the reverse direction and don’t think about alignment when making your character. Deciding what kind of character you want to play and then working backwards for their alignment is perfectly valid. Of course, it kind of makes you wonder why you need to even bother with alignment, but I find that it's a good exercise because it forces you to think deeper about your character. Since I've given some examples, I've found that lawful neutral with an evil bent can also be fun to play and be a part of. The player I know who did this last described it as someone who is lawful neutral but has grown bitter and a tad selfish through circumstance and bad fortune. Typically a good question to ask is “why is my character not this other alignment”?
What's It For?
A good thing to think about with any mechanic is why does it exist. Alignment is similar in this regard. Could we play just fine without worrying about alignment and coming up with characters on our own? Sure. I've seen it work. However, alignment gives us a starting point and helps us examine the motivation of our character. To assign an alignment to your character you need to think about your character. As a result even if I don't agree with your interpretation, it may have helped you think about your character's motivations and how they think. It is also something you can reference later to you help you play your character. It can be surprisingly helpful after a month or so break.
I find it is a very useful thing for a Dungeon Master. Of course it isn't as specific as we sometimes might like but we Dungeon Masters play many different characters over the course of a session. This little short form is extremely useful to get the gist of who your character is. You probably won't have time to define every henchman in the dungeon. However, you can give them an alignment and work within it as the game goes. Being able to reference something and having a starting point to work from makes it easier for me to improvise on the fly. I find that again, this is one of the hardest parts of improvising for me: trimming all the possible options I have for a character down to something useable quickly. And alignment is one tool in our arsenal for this sort of thing. In this regard it is especially useful for running adventures envisioned by someone else. An alignment, goal, and couple of mannerism and you’re well on your way to having a character in less than 20 words.