Stupid Neutral
Stupid Neutral is a term derived from the Dungeons & Dragons alignment system, but can easily be applied to characters in any role-playing game in fact, it can be applied to characters in any medium, or even real life for a specific way of playing a absolutely "neutral" character.
Definition
Much like Stupid Good which is Good for goodness sake, and Stupid Evil for evils sake, Chaotic Stupid for the sake of being chaotic and Lawful Stupid in following the law even when it doesn't make sense. Stupid Neutral is perhaps the most retarded and represents neutrality for neutrality's sake.
Normally, players who play a neutral character will behave ambivalent towards good/evil or law/chaos depending where exactly on the axis they sit, but would still have at least one aspect of the alignment to guide their actions (ie: Neutral Good) so can't really qualify as, or ever be Stupid Neutral (though kudos to the Chaotic Neutral player who tries to pull it off)
This means that Stupid Neutral players generally gravitate towards only one alignment: True Neutral. But there are a number of problems maintaining that "True" neutral status and playing it in a stupid manner... and that problem mostly surrounds the fact that as sentient creatures, we all understand the concept of morality and law, even if we as people don't agree with them. So people who espouse "Neutrality" generally either accept it and work with it, or can't be bothered by it and events happen anyway.
"Proper" Neutral would be more reactive, basically not going out of your way to do anything evil or good and just getting on with things like a normal person, if a sweet payday comes up that requires killing a few folks, you do it since you need the money and you think you can get away with it, rather than for any ideological reason or out of a desire to kill, then you pay your lawful taxes because to do otherwise just invites trouble.
Stupid Neutrality requires either being active about it (ie: a conscious desire to maintain a neutral status) or absolutely passive (ie: you don't factor important things like consequences into your decision making at all).
Passive Neutrality
Ambivalence towards alignment generally implies they are not bothered by it, so a True Neutral player who doesn't actually care about good vs evil or chaos vs law might as well just be Chaotic Neutral anyway, since they are going to make decisions based upon whatever suits them at a given moment in time and can be trusted to have the same moral capacity of a chimpanzee. These are the sorts of people who rationalise stealing your shit because they "needed" it rather than out of any particular sort of malice or avarice, but unlike an animal he actually understood the moral and legal ramifications of his actions and did it anyway.
It could be possible in gameplay to actually play this version of True Neutral to the point of Stupidity, but generally speaking, your GM cannot really account for your intentions, and only your actions. One can make the argument that following the law does not necessarily make you lawful, and that's true, but willful disregard for the law (even if you aren't breaking any laws at that given moment in time) is a chaotic mentality, especially if you know and understand the laws you're breaking and the consequences of doing it. For instance, if you do steal something or injure/kill someone who was only doing their day job, and then knowingly put that person or their family out of business and you don't really care about it then you've probably done something evil. However, if you justify that your need was greater (irrespective of any greater good) even then you still can't really escape the fact that you've probably done something chaotic.
Of course it is possible to play passive neutrality without being stupid about it, but likely that renders you an uncontroversial civilian bystander and not a sword-toting heroic adventurer.
One can also view passive neutrality, good or bad, as a sort of Skyrim-PC mentality. Accept quests from everyone, whether you agree with them or their organization, make no enemies (or as few as absolutely possible), and generally avoid conflict, taking a stand, or killing anyone who might have a job for you later.
Active Neutrality
This is where Neutral gets really stupid...
WANNABE True Neutral players are making a stance on neutrality, as if the cosmos needs to keep good and evil in a state of balance and that neither is better than the other. But if a mystic balance needs to be enforced to the point of anal retention and the player is the sort of obsessive person who will tell his compatriots that they need to stop being so good or lawful because the universe is keeping score and needs the balanced tipped carefully in the other direction. If all you are doing is see-sawing back and forward on the alignment axis in an attempt to maintain some semblance of balance, then you've become Lawful Neutral just yourself since all you're doing is imposing or restoring the Universal order. Also, if you ever start beating up Angels because "the universe needs balancing out", then that's pretty much evil in itself, especially since Angels probably weren't going to go out of their way to do you any harm unless you do something REALLY bad to piss them off. On a similar note: players who kick a puppy just to counter-balance their "good mojo" and force themselves back to neutrality are chaotic plain and simple and can just fuck off.
It's pretty well established that sparing the bad guy makes you the either the good guy or the lawful guy (or both), but don't even think about arguing that saving the BBEG's lieutenant or son or whatever so that the threat of their possible return will keep the forces of Good on their toes in future and not become incompetent from having nothing to fight! In this situation you're committing an evil act by rescuing someone that you intend to go on and hurt people in the future and give the forces of good something to fight against, or you're committing an act of good that's so convoluted that it falls squarely into the realm of Stupid Good. Either way, if you have to plan years in advance for something that doesn't directly affect you, chances are it's not a Neutral action. Best case scenario in this situation? walk away, but that's hardly "actively" promoting neutrality isn't it?
Basically what we're saying is that anyway you look at it, the only way to be Truly Neutral would to be an actual animal who has no understanding of morality or law whatsoever, either that or someone with a retarded level of intelligence. The only other way to truly stick to neutrality would be to spend your life having no impact on anyone or anything whatsoever.
Non-Stupid Neutral
A true neutral character without stupidity is possible, of course. Some examples include a character motivated by enlightened self-interest ("I will save the world because I live here and keep my stuff here."), a character who is playing the angles ("The world is full of powerful factions and I would rather work with the slavers and crusaders than try and overthrow them.") or a character motivated by an art or science ("I wanna be the very best, like no one ever was.")
Examples
- AO from the Forgotten Realms probably fits the bill, since he sits back and eats doritos all day, not bothering about anything in the multiverse, whether gods are killing each other or not. Only stepping in when the universe stops working properly and fixing it like a cosmic janitor with infinite power.
- Advanced Dungeons & Dragons actively describes True Neutral in Stupid Neutral of the "actively sabotages good, evil, law and chaos when they get too powerful" terms.
- Mordenkainen (basically the Greyhawk equivalent of Elminster), actually lives by the Stupid Neutral creedo of "Good, Evil, Law and Chaos are all dangerous if they are allowed to get too strong, so the best I can do for the world is keep them balanced". He runs a secret society dedicated to fucking shit over for whoever or whatever he thinks is being too successful and "threatening the Balance". Perhaps fittingly, he's an Abjurer and his legacy spells all relate to wrecking magic - the buffs-eating Mordenkainen's Warding Whip, or the magic item-killing Mordenkainen's Disjunction.
- Played for laughs in Futurama with the Neutrals: a race of aliens whose gimmick is that they act as neutral as possible. Live Free or Don't.