Stupid Neutral

"Good, they're both dead. The Balance has been preserved."
Or...
"Meh, so what if I refuse to try to put out this fire? As long as I can finish this post, I'll be content. I mean, I'm gonna die someday, so what if it's a little sooner than later?"

Some True Neutral people are devoted to the Balance Between Good and Evil - They fight only because the forces of darkness grow too strong. The problem comes when they become militantly neutral; so devoted to not taking sides that they lash out against both Good and Evil without distinguishing between Friend or Foe. This usually takes the form of always siding with the underdog; the moment one side gains the upper hand, they'll pull a Face Heel Turn (or a Heel Face Turn) to make sure both sides are 'equal'. This can lead to a very unreliable fellow and a Wild Card whose misguided morals lead his former allies to cut him down despite his protests that he was only following his heart.

Stupid Neutral people tend to think of morality as balancing a metaphysical checkbook; any evil deed can be 'cancelled out' by committing an equally good deed. No remorse or atonement is needed; to these people, there is no Moral Event Horizon past which their actions cannot be forgiven by good works (or evil works, as the case may be). In short, these people are the types who will build an orphanage and then "balance it out" by burning down the orphanage across the street. This pattern of kicking the dog and then stopping to pet it immediately afterwards just results in a very neurotic dog... and a very confused audience.

This type of "stupid neutral" may occur in Video Games with a Karma Meter that offers no true middle ground between 'Complete Monster' and 'The Paladin'. So the 'neutral' route, if it even exists, ends up consisting of doing enough good and evil deeds (with no regards to common sense or reason) to balance the meter in the middle. Or, you know, not doing anything, but where's the fun in that?

There is also the reverse of this in the other type of neutral, so neutral that they refuse to try to get out of the burning building.

Compare Golden Mean Fallacy. May be considered an unstable middle ground between Lawful Stupid and Chaotic Stupid.

No real life examples, please; there's no reason to celebrate people like this, even though we all know someone who probably qualifies.

Examples of Stupid Neutral include:

Literature

Probably one of the most well-known examples is Meursault, from The Stranger, who shoots an Arab because he sees no reason in doing so (the text implies it's because the sun was in his eyes), being an emotionless shell to all the wrong people before that, and not caring about anything in jail, awaiting execution.
In Villains by Necessity, the True Neutral druid rounds up a bunch of "villains" (most of whom are pretty decent sorts) to save the world from destruction at the hands of Lawful Stupid Knights Templar, and advises them that she would be equally willing to turn against them if the "balance" began tipping in favor of evil.
- In her defense, the world was about to be destroyed in a flash of light by the imbalance. The other druids, on the other hand, were pretty dumb betraying the massive forces of good in an attempt to save evil before it got to that state. Wouldn't it have been smarter to retreat, bide their time, and just do what Kaylana did?
Older Than Print: Early on in Dante's Divine Comedy, he meets the Uncommitted, who refused to choose good or evil in life, and as a punishment are forced to eternally chase after a banner while being stung by wasps.
In the Malazan Book of the Fallen the Forkrul Assail seem to have fallen into this category. Their entire culture revered harmony and balance to the point that when war broke out between the two other ancient races they would aid whichever side had the balance least in their favor.
- For an idea how well this policy worked out for them, they're functionally extinct in the present.
The troop of Dwarfs we see in The Last Battle. They don't want the heroes or the Calormenes to win, so they shoot at whichever side seems to have the advantage. "The Dwarfs are for the Dwarfs." It doesn't work out well for them, when the Calormene reinforcements arrive.
Lord Gro in The Worm Ouroborous just can't help rooting for the underdog, which leads him to switch sides on a regular basis until in the final battle he starts attacking both sides at once.
Bisochim the Wildmage from the Enduring Flame books brought evil back into the world and re-created the Endarkened, simply because he thought the Light was becoming too powerful and wanted to restore the True Balance. He gives many metaphors about how "light" blinds and burns and "darkness" is a desert-dweller's friend, but never gives any concrete examples of how evil could possibly be useful.
The Douglas Adams book Mostly Harmless features a race that is almost indistinguishable from human beings, save that they have no desires. Arthur reads one of their books, and is rather taken aback when the main protagonist dies of thirst midway through. He backtracks and finds a single offhand reference to the character's plumbing being broken. He simply didn't care enough to have it fixed, or to seek another source of water.

Live-Action TV

The royal court on Kings bounce David around so much—changing alliances, pitting him against each other, it feels like they change sympathies solely to hammer into you that it's a morally ambiguous world.

Tabletop Games

This is the MO of the Rilmani of Dungeons & Dragons. They're anthropomorphic personifications of the Balance, and will take steps to ensure that balance.
- Early editions of the game strongly suggested that this is how druids (who were always supposed to be true neutral) should behave, basically stepping in to support whichever side is weakest in any given situation. 3rd edition relaxed things a bit by requiring druids to be only partially neutral, implied that their previous methods (flip-flopping one's agenda and allegiances) fostered chaos more than anything, and suggested that true neutrality was more about detaching oneself from concepts of ethics and morality than about maintaining an arbitrary balance.
  - This still seems a bit odd, however, as somebody with no morals or ethics is going to be chaotic evil. The alignment system in D&D is usually fairly easy to understand, until they try to explicitly describe True Neutral (which also includes things too dumb to have an alignment, and also presumably Cthulhu and friends who operate on Blue and Orange Morality). Despite this, the general trend seems to be going away from Stupid Neutral and Lawful Stupid.
    - Having no morals doesn't necessary entangle being a monster. It can be a worldview that morals have been essentialy made up by demi-humans (let's ignore for a moment fact that it doesn't make much sense in D&D), and they don't want to be constricted by either good or evil. Doesn't mean they get high from killer sprees, maiming and burning, just "live and let other live".
    - The most sensible interpretation of True Neutral is that they are just "normal people," willing to break the law or do somewhat evil stuff, but only if they really have to.
- Mordenkainen the Mage is the original incarnation of this trope. He believed that the forces of good, evil, law and chaos would all screw the world up if they were unquestioned, so he ensures that no side is ever vastly more powerful than its counterpart.
- Versions 3.0 and 3.5 explicitly point out that PCs playing "true neutral" shouldn't fit this trope. Even though they usually don't care about greater causes, true neutrals still prefer neighbors who aren't going to betray, kill, or enslave them.
- According to some sources, the concept of a "constantly flip-flopping character" trying to maintain True Neutral is either a case of an overly strict DM or an unimaginative player: a neutral druid would absolutely take up a series of quests to oust various evil/chaotic influences, but only when those evil influences would tip the balance far too far in away from good/lawful. The balance they (are supposed to) seek is the balance of the WORLD, not themselves.
  - This type of argument is also one of the specific reasons they streamlined the alignment system for 4e, and came up with "unaligned", which basically boils down to "works for themselves rather than any particular ideal", and the only way to change alignment is DM-contrivance, permanent mind control, or player's choice, rather than simply "you did too many good deeds in a row, now you're not allowed to pickpocket random strangers."
Nix from Queen's Blade isn't the stupid one; rather her stave, the Funikura, is essentially an unstable piece of work that can either destroy a village or kill the evil leader of said village. Needless to say, she sticks with it.
Rounding out the Warhammer 40,000 Inquisition examples: the Amalathian faction are the ultimate conservatives, believing that the Imperium as it currently exists is the Emperor's divine work, and that mere mortals have no right to interfere with His divine plan. As such, the Amalathians fight to preserve the Imperium in its current state, despite all its lumps and imperfections. At their most extreme, the Amalathians will even fight to keep corrupt or ineffectual leaders in power, simply to avoid the inevitable shakeup associated with replacing those leaders, even in the face of an ensuing crisis that requires effective leadership. As you can imagine, Amalathians and Recongregators don't get along very well.
Rifts creator Kevin Siembieda has said that the last part (not getting out of a burning building) is the reason the Palladium Rules System has no Neutral alignments. His opinion is that Neutral characters would be unwilling to do anything interesting, like adventuring.

Video Games

This is the only way to have a neutral character in Fable due to how combat works. After several missions (most of which don't have an evil option) you'll be so far to the good side of the Karma Meter that slaughtering an entire village barely gets you halfway to the middle.
Probably the best example is Neverwinter Nights and its expansions and sequel. It is damn-near impossible to keep a True Neutral alignment because there never is a neutral option to dialog, so you're acting either as a jerk (evil), a loony (chaotic), the messiah (good) or a robot (lawful), and to try to keep a balance there will make you seem bipolar.
In Fallout 3, the Impartial Mediation perk gives you 30 bonus points to the Speech skill (an extraordinary amount) as long as your Karma level is "neutral". Since, once again, Karma is a scale between good and evil, with no specifically "neutral" actions, you will probably be forced to alternate between stealing and murdering and giving to charity to maintain a neutral Karma.
In Marathon 2: Durandal, the Jjaro AI Thoth aids Durandal's (and by extension, your) cause with the reasoning that you're at a serious disadvantage against the Pfhor hunting you down. Then when things start going your way he tries to thwart you and aid the slaver race but Durandal has tipped the scales too far in his favor for Thoth to make a difference at that point.
- It's implied that a major part of the problem is that the Pfhor aren't much inclined to listen to the AI that was just helping you kill them. Its schizoid side-swapping put a serious dent in its credibility.
  - To further complicate the issue is Durandal's reputation to screw over anyone and anything he can in order to achieve his often enigmatic goals. Thoth wasn't trying to balance good and evil, he was trying to strike a balance between an Evil Empire and a psychotic Master Computer with its own agenda.
In Shadow the Hedgehog it is perfectly possible to be Stupid Neutral. One of the better examples is that you can raise the flying temple of Black Doom. Then you can quite easily work your way to a level where you have the option to bring it crashing back down again. Or you can try to stop it from rising, and then go on to keep it airborne.
In many early MUD games, alignment was determined by what monsters you were killing. Kill some innocent Gnomes in the Gnome Village, and your alignment shifts towards evil. Kill some Lamias in the ruins across the forest and your alignment shifts towards good. Neutral characters, to maintain their alignment, had to kill an equal number of creatures from both alignments. This lead to "Neutral" characters being "justified" for massacring a peaceful village by simply cleaning out an evil temple later. Granted, you could seek out and kill only neutral creatures all the time, but these (usually animals) obviously almost never carried many powerful items.
Planescape: Torment features a character called Blackrose, who lurks in the corner of a dangerous alley. In the alley are two gangs, one good and one evil. Blackrose will ask you what your alignment is, and ask you to kill the opposite gang. Once you've done that, he'll ask you to kill the other to maintain the balance. Then he'll request that you fight him to the death because it's the right thing to do. You can at least avoid the fight to the death by informing him that you're immortal and would eventually win.
Averted in The Witcher where the the neutral choice between one side or another simply means not accepting a quest or refusing to complete a quest (though may be boring since you didn't actually do anything.)
- Also, there's a third option for the civil war between the Scoia'tael and the Order of the Flaming Rose: you can in fact remain neutral.

Web Comics

The Archdruid in Dungeon Crawl Inc. He's an evil antagonist (despite technically being neutral at this point) specifically because... good is somehow too prevalent in the world.

Web Original

This sometimes pops up in Survival of the Fittest with non-players who refuse to attack anyone under any circumstances (at least one person has died because they refused to defend themselves).
This seemed to be the concept behind a majority of the neutral route players of the game Nexus War before it shut down. you learn to stop trusting "neutral" players rather quickly after the counter for Myrmidons that have senselessly slaughtered your Good character in the night hits double digits.
- The Nexal Champion class even got impressive bonuses to attack and damage for staying as close to 0 morality(min and max values being -40 and 40 respectively) as possible
Arguably the staff at Whateley Academy are bordering on this. While their desire to provide a safe haven for the superpowered children of both heroes and villains is understandable, their execution of their policy leaves much to be desired—turning a blind eye to some of the criminal and even outright vicious behavior of many "ethically alternative" students, hiring staff of criminal and even murderous backgrounds, welcoming an Eldritch Abomination prophesied to destroy all humanity as a student.....
- Part of the issue is the Whateley Charter—the details on which are sketchy, but is an agreement between Superheroes, Supervillains, and Superneutrals to make sure Superpowered children are safe. Presumably, the Supervillains would have made absolutely certain that part of the charter included turning a blind eye to certain amounts of villainy—remembering that for a villain, learning how to sneak behind authority's back is a vital life lesson. Ultimately, the one thing the Superheroes, Supervillains, and Superneutrals could agree on was going after friends and family is beyond the pale—the only way to make sure everyone wants you dead in the setting is to break that cardinal rule.
  - Unlikely, a neutrality agreement means no crimes or crime fighting. Anyway you don't learn anything about sneaking behind authorities back if they turn a blind eye.

Western Animation

Equinox, a vigilante on Batman: The Brave and the Bold. He tries to kill Gorilla Grodd for his crimes, but in order to "maintain the balance" he tries to kill the Question at the same time.
- Based on Libra, from the main DC Universe, who also "maintains the balance", but what that translates to is "giving the baddies some wins."
The Neutral Planet in Futurama is a deliberate parody of this alignment.

Neutral President: I don't know, but my gut says "maybe."
Neutral President: If I die, tell my wife, "hello."