Ronnie Schiatto from Baccano! is just as likely to incite a massacre as he is to follow a man for two-hundred years just to give him some company. The only answer he's ever given for his motivations is that he's very old, very powerful, and very bored.
Similarly, Huey Laforet. The amount of regard he has for human life is determined by how much scientific knowledge they provide.
Ladd Russo, believe it or not, does have some set of values. It can best be described as thus: Life is fleeting, and people are liable to die at any moment. People who don't understand this need to be taught through direct experience - aka dying.
Elmer C. Albatross's moral axis doesn't take into account things like "good" or "evil". All he cares about is happiness. Seeing other people happy makes him happy, though he doesn't actually care about the people. This makes him a bonafide sociopath with a mindset so alien and disturbing that it terrifies the Big Bad.
Black Hanekawa chides Koyomi from Bakemonogatari for thinking he can befriend or empathize with so-called "oddities" such as itself. Koyomi frequently repeats that oddities should not be hated for what they do because they're only doing what is natural for them.
Bleach: Mayuri is the ultimate scientist of the series, lacking his good counterpart Urahara's morality and his Evil Counterpart Szayel or Aizen's god complex. All that matters to Mayuri are results; he doesn't seem to see any sort of hypocrisy in torturing Quincies to death as a form of study and then healing the last remaining one years later to show his new medicine works perfectly. He abuses his daughter, but from his own perspective this is because he knows for a fact his creation can handle it and people protesting how he treats Nemu are questioning the quality of her design. Szayel raping and nearly killing Nemu to save himself from death doesn't appear to bother Mayuri (he can just "fix" her later), but he expresses utter contempt for him once he hears Szayel proclaiming himself a perfect being; perfection would be the death of scientific innovation, after all, and no man of science should view that as desirable.
Nathan Mahler of Blood+ is less than concerned about the ongoing war between the Red Shield and Diva's group. His true motives aren't revealed until the very end of the series, and are cryptic even then.
Death Note: The Shinigami. Their existence revolves around killing human beings, and they need to do it to survive. Their greatest sin is to kill someone to preserve the life of another, which is apparently too close to playing God. Ryuk dropping the Death Note onto Earth out of boredom seems pretty cruel, since it turns Light Yagami and others into callous killers, but to him, killing people with a Death Note is just a part of nature. Shinigami might be a subversion, since they seem to understand and comprehend human emotion and values perfectly. Ryuk is well aware that Light is a monster and calls him out on it, but just doesn't care. Which makes a certain amount of sense for a nigh-immortal Shinigami; we're all going to die soon anyway so why should he care if some of us die a few decades earlier.
The D-Reaper from Digimon Tamers is a prime example of this trope, acting on its former programming (Deleting anything that has evolved beyond its parameters) and being absolutely terrifying about it without any real intentions. This changes once it learns about human morality though...
Dragon Ball Z: Battle of Gods: Beerus, the Big Bad of the film, overlaps this with Jerkass Gods. He's the God of Destruction, it's his job to destroy worlds so it makes sense he doesn't see anything morally wrong with his actions. It's actually established that old planets have to be destroyed so new planets can be born; the problem with Beerus is that he acts independently of the Kaioshins (even worse now that there's only two of them left), chooses what planets that he will destroy at his leisure, and he can and will destroy even important planets without a second thought if he's irritated enough. Super introduces his twin brother Champa, the God of Destruction of Universe 6, has the same type of morality and it's implied that these two are actually mellow by God of Destruction standards.
Every pure blooded Saiyan has this sort of morality, as it is in their nature to strive for a great battle no matter what the risk and such a behavior and mentality like that is questioned by several characters, good and bad, throughout Dragon Ball Z. In fact, Goku is a much more benign example than the rest of his Saiyan counterparts due to the head trauma he sustained as a toddler and being raised morally by Grandpa Gohan. The only character who probably has more of an "alien" view of how the world is perceived than Goku is Vegeta; considering that his desperation for a great battle has the been the catalyst for every single arc in Dragon Ball Z occurring. There is a reason why some fans consider him The Load. However, with his increasing amounts of Character Development post-Buu Saga, especially in Super, Vegeta is moving away from his primarily Saiyan mindset, which serves to all the more highlight Goku's continued alien mindset, such as at the beginning of the Universe Survival Arc, the latter not understanding the former's newfound desire to stay at Bulma's side, now that she's pregnant with Bra. Overall, Dragon Ball Super borders on deconstructing Goku's mindset, in the face of other fighters who've themselves changed, especially to Western audiences who grew up with his altered characterization in the original Funimation dub.
Word of God from Akira Toriyama is that Saiyans as a whole have a strange view of relationships and procreation as well. They don't generally have an idea of marriage, outside of royal bloodlines, and don't mate for romance but simply for procreation. The most Saiyans tend to feel about their mates and children is close friendship and battle companions, but not romantic, paternal, or maternal love as a human understands it. This is why Goku is a relatively poor parent to Gohan and Goten and husband to Chi-chi. It is very rare for a Saiyan to feel genuine love for their mates and children... which is why Vegeta's relationship with Bulma and their son Trunks is so much more special.
Izaya Orihara in Durarara!! works by an series of rules that seem to default to "I'm a troll" but have deeper and longer-reaching motivations. His morality seems to be guided simply by how boring something is.
Characters with Blue and Orange Morality are common in Ryogo Narita's work, to the point that it'd be harder to find the ones that are normal.
Kimblee in the Fullmetal Alchemist manga and second anime has an odd code which seems to consider holding true to your role or principles the most important thing, irrespective of their conventional morality. He criticizes soldiers for being reluctant to massacre defenseless people, but expresses admiration for the Rockbells for their determination to save lives (of the same people the soldiers were killing) as doctors. He sides with the homunculi because they give him freedom to practice his alchemy without restriction, but claims to be primarily interested in who'll win the conflict between them and humans. In the end he saves Ed from a Grand Theft Me by Pride because he's repulsed by Pride abandoning his claims of superiority as a homunculus to merge with a human to save himself.
Gundam 00 has the Extraterrestrial Liquid-metal Shapeshifters (ELS) from The Movie. These are intelligent metal-based life forms that evolved on a gas giant. They communicate telepathically, or by combining their physical forms together to form a unified being. Naturally there is some amount of extreme confusion between the two species when they meet humanity. The mutual misunderstandings lead to a war between the two before a clear means of communication is found.
Mercurians in Gunnm are the descendants of the nanomachine plague left on the planet by a terrorist half a millennium ago. They've since developed into the civilization so utterly alien to the humanity's way of thinking that their ambassador (or at least the entity supposed to contact the Solar System at large) turned out to be a 20 meter tall killing machine with a phallic-shaped Wave Motion Gun in the right place. Fortunately there were places where such "Ambassadors" could be dealt with.
Guu of Haré+Guu, essentially The Trickster. There seems to be no rhyme or reason to her actions: she's just as likely to torment Haré as rescue him from mortal danger by summoning godlike powers, all the while seeming casual and uncaring. Her inscrutable agenda makes it impossible to pinpoint her Character Alignment.
She loves to act like she's giving Haré An Aesop, but always subverts it completely in the end.
Ryoko Asakura (an "integrated data entity" disguised as a human) in Haruhi Suzumiya. She honestly can't grasp why murder is wrong as long as it achieves an objective.
Similarly, Kuyo Suoh. She (and the entity behind her) is simply so alien in personality that she makes Nagato and Ryoko look like normal human beings... to the point that when Kuyo makes her own attempt on Kyon's life, it's Ryoko who saves him.
Vampires in Hellsing (more the anime than the manga) are alluded to having their own set rules and motivations, this is what made the Freaks so dangerous since they were artificial vampires and thus had vampire powers but human desires and instincts. Vampires such as Incognito and Alucard seem to have taken human masters in part for this reason.
This plays a large role in Heroic Age, in which the "Iron Race" (humanity) doesn't understand the values of the "Silver Race" that is warring against them, especially considering that they are Straw Vulcans who reject/transfer emotions to a few chosen individuals. The lack of understanding that the SR have no emotional attachments (to home planets) while humanity does, causes the SR to wonder why the humans would try to take back their home planet and then try to conquer the homes of the "Bronze Race" and SR, and causes the human military to attack what they assumed was a well defended BR home world when it was a weakly defended mass nursery, and attack the SR homeworld which was mostly abandoned, opening themselves up for an ambush.
Gon Freecs has distinct shades of this. He isn't The Unfettered, because he is guided by a strong sense of right and wrong, but as the counterfeiter he hangs out with finally realizes, "He doesn't care about the good and the bad." Mostly it's enough to peg him as Chaotic Good, but that doesn't really do him justice. Neither the readers nor the other characters can really predict where his moral sense will take him, and he surprises even his best friend (a child assassin) a lot. Notable events include:
A serial killer once trained him and Killua, and he cheerfully allowed the person to go free afterward even after it was pointed out that this would cause more young women to get eaten, because "he helped us."
After one of the Phantom Troupe is killed by Kurapika, Gon and Killua are captured by his best friend, who suspects them of involvement and rants, in tears, about how much it hurts to have lost his blowing-stuff-all-to-hell partner. And Gon responds with sudden fury, because he had assumed that the Troupe's members could do such horrible things because they didn't understand how much it hurt to lose people, which meant he couldn't hold it against them, but if they can and still do it they're so incomprehensibly evil he wants to end them.
Tonpa admits how much he enjoys watching people fail miserably and die taking the hunter exams, which infuriates everyone else... except Gon, who continues treating him like a friend because he inadvertently helped them with his cowardice.
There are several times where Gon puts a mission, and even his friends, in jeopardy because of his Blood Knight tendencies and a bruised ego.
During the Chimera Ants arc Gon's main objective is avenging Kite, and when Neferpitou, the ant responsible for Kite's condition, begs him for more time to heal Komugi, an innocent blind girl caught in the middle of the whole conflict, Gon flies into a rage over Pitou mutilating his beloved mentor yet showing compassion for someone else, and completely disregards Killua's feelings about the situation. He gives Pitou less time than requested, reduces the amount of time for every distraction, and even threatens to kill the mortally wounded Komugi if Pitou tries to make a run for it. Gon only lets Pitou heal her after Killua reminds him that Pitou is the only chance he has at restoring Kite, and not out of any concern for Komugi's well-being. It's quite possibly the ultimate example of how Gon's morality is derived from his own experiences instead of any traditional sense of right and wrong.
The Chimera Ants enter this territory from time to time, as well. Though they're largely just evil. Although most of the ants are evil and some are good, the king, Meruem, is a master of this trope. All the experiences he goes through continually shape his moral code which fluctuates wildly through the arc, turning him from what appears to be a Cell rip-off into one of the most deep and interesting villains in Shonen manga. And yet he always seems to have his code stuck somewhere in the Blue and Orange territory.
Hisoka's moral code begins and ends with fighting. He isn't concerned with good vs evil or right vs wrong or even powerful vs weak (although he certainly factors that axis in) so much as finding and/or cultivating opponents strong or interestingly weird enough to give him the fight of his life, and lives for the satisfaction of killing them down the line. The world for him divides this way: Worthy Foes (to whom he is helpful and fairly, even surprisingly, polite to... in his own way) vs Unworthy Foes (not polite to, like, at all: so very, horrifically dead if they push his disgust or bloodlust even slightly) vs Rocks (just about everybody else — dead only if they become inconvenient or really, really tedious: Nothing Personal) vs Nopes (things that are just too many shades of dangerously alien for him to find any merit in messing with — rare, but it happens). Treating him as both Faux Affably Evil and Chaotic Evil are the safest things to do, but... They're not entirely accurate.
At first blush, the entire Zoldyk family seems to share a fairly Lawful Evil, Consummate Professional code — they kind you'd expect from a family of assassins. It colours everything they do, from Training from Hell kinds of Tough Love to a very flexible outlook on violence. But, the more you get to know about them, the weirderitgets and the less of a convincing "typical moral spectrum" they show, even for the deeper, darker, more Evil parts of the pool. Killua is the most normal of the lot, thanks to wanting to branch out and engage with the wider world... Yet, he is his own brand of off-the-wall, too. And, then there's Illumi. Oh, boy; he takes the family weirdness to places even the rest won't willingly go — he's after power at any price... when the rest of the family is basically about charging other people a mint to kill people, not the power trip.
The Pillar Men in JoJo's Bizarre Adventure have little to no regard for human life, other than the occasional human warrior who knows how to use the Ripple (which is their greatest weakness), but their leader, Kars, will go out of his way to not land on a patch of flowers, or kill some teenagers so they don't run over a puppy. Unfortunately, he later Jumps Off The Slippery Slope even for their standards. Whether this was the mindset of the entire Pillar Man race is uncertain. They apparently lived in relative harmony with the rest of life on Earth and each other. They even tried to kill Kars because they believed his ambitions endangered all life on the planet.
The title character from Majin Tantei Nougami Neuro exemplifies this trope. His one and only concern is discovering and solving the mysteries he feeds upon. This, mixed with the fact that he is a demon, make for a very unique morality in which he likes and protects humans, not because it is the right thing to do, but because they provide his food and entertainment. That by no way means he can't have fun at the expense of humans, though.
Minerva-X from Mazinger Z is a sentient Humongous Mecha specifically created to be Mazinger-Z's Battle Couple. Despite -or maybe because- she was created by humans, several of her personality traits -mainly her conception of what love is- are completely bizarre. Because she was created to be Mazinger's partner in battle, she is in love with Mazinger in spite of she knows it is a machine and it is not sentient. She also treats the pilot of a Humongous Mecha like if it was another part of the mecha (presumably, the brain). This is expanded on Shin Mazinger Zero, where she (transformed into a Robot Girl) teases Sayaka because she saw Aphrodite (Sayaka's Fem Bot) fighting alongside Mazinger and got jealous, got... all bothered when she was inside Mazinger's cockpit, and she told she loved Kouji... but she loved even more Kouji piloting the Hover Pilder, and she loved above all Kouji on the Pilder piloting Mazinger. Usually Kouji and Sayaka only shake their heads and accept her like she is.
Sayaka: How... unique...
The eponymous Mononoke, from the show of the same name, are repeatedly stated to think completely differently from people. Depending on the incident that created them, their thought process can be very, very warped.
The more intelligent mushi of Mushishi are a milder case. The mushi's form of life is so alien from our own that 'good' and 'bad' may mean completely different things to us and them. For example, in the very first episode the mushi lure a young girl out to the forest for a feast, during which they tell her that they want her to watch over her future grandson. Ginko himself makes no comment as to whether he thinks she and her grandson will be better off with the botched mushification completed or not; he merely presents each of them with the option of completing it and lets them decide for themselves.
Kyubey of Puella Magi Madoka Magica is stated to be unable to understand human morality, being utterly confused as to why the girls would be horrified by the idea that a contract with him is essentially lichification. He later states that the species that he belongs to is incapable of emotion of any sort. In terms of actions, he also sees nothing wrong with manipulating generations of girls into situations that inevitably lead to their becoming murderous Eldritch Abominations, since the system prolongs the life of the universe by reversing entropy. He also doesn't understand why humans consider omitting important information as a form of duplicity. Although he is quite clearly aware of what humans think of his actions, hence his duplicity. He just doesn't get why we think that way.
A lot of the swordsmen in Vagabond follow their own personal codes of honor, and the story doesn't really present Musashi as "evil" because he kills people.
The second chapter of World Trigger has Kuga, a young boy from another dimension, walking around Japan doing things like offering his classmate a large wad of cash when he offers to take him out for dinner, breaking a mugger's leg, then simply knocking out another group of muggers when he's told by his Ordinary High-School Student friend that what he'd done was excessive, and offering compensation to a woman who'd crashed her car into him. He healed himself almost instantaneously, so it was likely for the car damages.
Yuuko from ×××HOLiC could be considered to have a version on this, in which, to Yuuko's point of view, any wish or decision can be justified, as long as the the wisher or decision-maker is satisfied with the result, and the only rule in her wishes being Equivalent Exchange and that she won't kill, as it will 'weigh down' on the Universe.
Some supernaturals falls under this trope as well, for example Jorogumo directly states that she will not take anything that was given to her, but when Watanuki (the protagonist) fights for his goal, she clearly approves and leaves. All the time with a cheery attitude and threats of murder.
Watanuki adopts it as well at the end of the manga.
Togashi makes allusions to this in YuYu Hakusho, too, once the S-Class demons start to turn up. Previous, all the weird-thinking people like Sakyou and Sensui were insane or just evil.
Parasyte: Parasites eat humans because that's how they survive as a species, and they feel no more guilt about killing the sapient lifeforms who serve as their prey than humans do about eating livestock such as pigs and cows. They are mostly incapable of emotion, so whenever they explain the reasons behind their actions it's very cold-blooded and matter-of-fact. Furthermore, each individual of their species will do anything to ensure its own survival, and they do not understand the human concept of altruism. Migi is frequently baffled by what he sees as irrational behavior and thoughts from his host Shinichi, and considers Shinichi's objection to plans he suggests—like using his classmates as human shields in order to defeat a hostile parasite, or even just pickpocketing money to purchase a cab ride to safety—to be a misguided case of Honor Before Reason.