In The Adventures of Dr. McNinja, the residents of the Radical Lands base their morality on how cool something is. Ron Wizard's response to being summoned to a boring world is You Monster! Conversely, they have no qualms about harming or even killing innocent but boring people, and do so all the time in the name of Rule of Cool.
Pretty much everyone the protagonist has encountered in Awful Hospital, and most of the comments section, as well.
Sam Starfall of Freefall seems to fall into this. He explains that, coming from a race of scavengers, morality on his homeworld is incompatible with that of human society — stealing, for example, is seen as an act of bravery necessary to help your family survive, especially if done from a stronger scavenger or a predator. But at the same time, he revels in breaking the law just for the thrill of it, so he may just be using the scavenger morality thing as an excuse.
He also takes this view of the humans. Florence and most of the robots are considered "property" because they're created by humans—AIs, even if one of them is made of meat. But on Sam's homeworld, the ownership of a sentient being would be considered unthinkable.
The family life of Sam's people counts as well. They die after mating, so the only ones who live to adulthood are those that are sterile. When new nests of infants are born, adults come around and adopt them, like picking up a free kitten. Only a few are related to the people who raised them.
The main protagonist, Florence Ambrose, is a genetically-modified anthropomorphic wolf, so her social interactions tend to be based on pack mentality and behavior, as well as trying to satisfy leftover instincts while fitting in to human society.
In The Order of the Stick, we see Nale Comically Missing the Point of his Succubus companion's displeasure, though he recovers quickly. Likewise, it never seems to occur to her that Nale might not like hearing about how she had sex with other people four times in a mere three hours — she actually thinks that he is surprised by how few people it was, justifying it by saying that she "had errands to run, too."
There's also Elan's attempt to make a decision based on the principles of pure Law and Chaos:
Modron: 100101010100010101101011!note This is binary gibberish. In ASCII it would be:"_-k" Slaad: Turquoise bicycle shoe fins actualize radishes greenly!
It's starting to look like it's genetic, given that their father, Tarquin, has a morality entirely built around what sounds good from a narrative perspective and, as such, considers killing to be a perfectly reasonable method of removing obstacles, but he thinks it's unforgivable that his Good-aligned son Elan is the Bumbling Sidekick instead of The Leader. This goes to the extent that he's styled himself as an Arch Nemesis Dad for the sole reason that it makes the story of him and his sons more dramatic. He also has no problem that Elan might wind up killing him. In fact, he thinks this is far better than Nale just being Elan's Evil Twin since it means Elan and Tarquin will get to have an epic final showdown between father and son, and that kinda stuff is gold!It's the ultimate insult when Elan leaves him, alive but defeated, in a desert - instead of killing him outright. Now, instead of being remembered as the villain of a grand tale, Tarquin will be a laughingstock... and worse, forgotten.
If what we're told about the Snarl is true, it doesn't kill because it's malicious. In fact, it can't even understand the act of killing, because it doesn't understand orderly concepts.
Sparks in Girl Genius regularly slip into worldviews that for normal humans would be... err... ratherunusual. The Jägers, as well, have very odd values: while they would rather the Lady Heterodyne acted like her "fun" murderous ancestors than the heroic Bill and Barry, they detest The Other as much as everyone else, not for being evil, but for being no fun to serve; still, the softer Heterodynes are good enough, as is the order-minded Klaus as long as the Heterodyne succession is uncertain. The castle's attitudes are similar, albeit a bit more sadistic.
Kevin & Kell: The rules there are way different from ours, simply because animals are sentient. For example, Kell (a wolf) works for a corporation whose business model is hunting and killing people for use as food. She only objects to hunting species that she's related to, notably rabbits, as she might end up eating one of Kevin's relatives (she apparently ate Vern and Betty Lopear, two rabbits he knew, a while ago). According to the FAQ, there are some rules regarding killing, though, as predators can only kill prey for food, and if herbivores kill, they must prove that it was in self-defense.
One storyline involves the main characters finding a body and being horrified to realise it hasn't been eaten; it was murder!
Doc Rat also features predation as a normal part of society. Different species seem to have different views on the matter- for prey, it's a constant worry (travel guides for rabbits point out how to avoid predators by species), and for predators there seems to be three main justifications: It's traditional, predators have the right to do so, and it's good for population control. There also seems to be a split between reptilian and mammalian thought, if Neil Dunn's attitude is typical of snakes.
Troll society in Homestuck falls under this trope; especially in regards to their romance, caste system, and concept of coming of age. Troll society is also much more violent than human society, so murder is less a crime and more of a faux pas — you're more likely to set off a nasty Cycle of Revenge than get prosecuted. Of course, if you do get prosecuted, then you're screwed, because on Alternia, every court is a Kangaroo Court.
Thanks to the incredibly weird way in which trolls reproduce, they have absolutely no concept of parenthood or familial bonds. Not even Karkat or Kanaya, the two most humanlike trolls, could grasp it after three years of cohabitation with Dave and Rose, even though they did their best to introduce the trolls to human culture.
It's eventually revealed that Troll society was deliberately made that way by an Eldritch Abomination.
Cherubs take it up a notch. For starters, they are incredibly solitary creatures, and their entire mentality is centered on being alone; they might not see another of their own for millenia. Also, their entire emotional spectrum is centered on hate, including their romance! To top it off, young cherubs are Mind Hives with a good and a bad self that take turns controlling their shared body. Then one of the halves commits Split Personality Takeover and assimilates the other half. It is downright said that the continous abuse, bickering and harassment from their alternate self is required for a cherub to develop a healthy psyche. They are so different from humans that fitting in with humans actually weakens a cherub's resolve and heightens the chance of getting taken over by their alternate half. Considering all this, you can understand why all cherubs are incredibly strange.
Gunnerkrigg Court: What are the grounds for a true and solid friendship between the fairies? Cool hair, it seems, since two alienated friends get back together after a haircut (much to the main characters' chagrin). The two aforementioned fairies, funnily enough, happen to be orange and blue-haired, respectively.
It's explicitly stated that animals of the forest "strut and bare their teeth," because that is how animals earn respect.
K'seliss from Goblins has no qualms about killing or eating people, but fighting against animated objects? That would just be sick!
Specifically, he sees no difference between killing, eating, and mating. Therefore, fighting something inedible is in fact a form of sexual deviancy to him.
The people in Collar 6 seem to have a wildly different morality system than the people in the real world, based on Atlantean writings. The system arguably resembles a very extreme form of libertarianism, with people able to sign "slave" contracts that give others actual legal authority over them.
Mistress Sixx is surprised at Laura's outrage at being drugged, put in bondage and forced to participate in sexual acts, since Laura had previously enjoyed participating in consensual sexual acts without bondage or drugs - not recognizing at least three differences between those cases. Apparently the author was called out on that by the readership, and was forced to make an Author's Saving Throw with Sixx apologizing for her inconsideration.
Demons in Wapsi Square have a strict set of rules which they follow, but those rules don't match up with our ideas of right and wrong. They even specifically mentioned that evil is a human concept, not a demon one.
Professor Joseph Corwin in Tales Of Gnosis College shows signs of this trope. He is more than happy to lure female undergraduates into weird experiments the involve changing their state of matter or intimate contact with tentacle beasts, but he draws the line at using is technology to make duplicates of people, even when that would be handy. He’s also intensely loyal to his own subordinate.
Raven's mother (sometimes called Chaos, other times called Pandora) wants to help her son out, so she begins to instigate many magical incidents, such as granting powers to unaware people leading to near-disasters when they unwittingly use them.
In Educomix, Ecoism (Jessica and Dave's religion) is portrayed as superior to the other religions in the strip (Euphemism and Ecotology), even though all their rules seem just as arbitrary as each other. Ecoists believe in never using water for anything except drinking to avoid damaging the "ecos", Euphemism appears to be similar to Christianity or Judaism (although they believe that Adam is still somewhere on Earth), and Ecotologists also want to save the ecos, but think that they can accomplish this by populating the country of Asia with clones of everyone from the rest of the world. The main Ecotologist even has blue hair to contrast Jessica's orange hair!
In the Space Arc of Arthur, King of Time and Space Arthur's attempts to make peace between humans and the alien races (Dragons, Stags, and Faerie) are stimmied by just how different their viewpoints are. Elaine suggests it's not just cultural, they're neurologically different. In the Space and Fairy Tale arcs, Morgan le Fey has long since realised that it's actually impossible to have an Evil Plan that involves Faerie in any meaningful way; their alien outlook appears to humans to be extreme Attention Deficit... Ooh, Shiny!, and isn't really compatible with any sort of planning.
In Roommates Jareth's dark side thinks in trope and measures moral questions in the terms of the Theory of Narrative Causality. He would kill if that was dramatically appropriate in the story and in character for his current archetype, maybe feel remorse about the life lost, but would think and feel that that was the right thing to donote (He pushed his best friend off the rooftop because he refused to be the "Hero" (ended up as one anyway) and Jareth was the "Villain" that time and that's what villains do). To clarify he seems to have some idea about what humans call "good" or "bad" but he thinks of them as storytelling devices not morality and as such doesn't value them over any other trope. Also his father seems to have similar notions so maybe this is the standard Blue and Orange for The Fair Folk in the series.
In the Spin-OffGirls Next Door even the guys normal personality is enough to produce ++CUCCUMBER ERROR++ on heaven and hell's Good-Evil'O'Meter.
Karl Tagon: You seem more outraged by what they do to data than what they've done to living beings. Petey: I love all kinds of data, and living beings are data that make more data.
The morphE universe (or the New World of Darkness universe that it takes place in) runs off of this. The newly awakened mages are incredulous when otherwise reasonable people like Malloy insist that Amical is a good person for plucking new mages off of the streets and raising them. Within the world setting he is doing them a kindness by protecting them from the various mage groups and supernal beings that would prey upon them in the wild. This doesn't excuse that he casually killed 3 people in the intro chapter and pit his new recruits against one another in a duel to the death.
William in A Hate Story is a Pure Magic Being that is extremely caring and protective of people he personally knows, but sees everyone else as immaterial and can't comprehend that strangers' lives have value.
The Binding from Sire is the force that turns the lineage children into Generation Xeroxes, forcing them to spend their lives studying to find their Aesops or else. Susan seems to be the first person to point out how messed up this is.
In Wizard & Giant™, Wizard and Giant are a pair of gay anarchists, perfectly willing to let a monster destroy most of a city, even willing to get each other captured by power-mad oligarchs for the purposes of a marriage proposal.
As the characters of Consolers are game companies, they sometimes put profits and business above what would be considered the more "moral" choice in human terms. Doesn't mean that some behavior isn't looked down upon by the rest of the industry, though.