Nekron from Blackest Night was intended to have this according to Geoff Johns, simply doing what he was created to do, which was bringing death to the universe and raising the undead, and being beyond understanding. However, his actions during the event such as controlling heroes' bodies as Black Lanterns with their consciousnesses being unable to do anything about it suggests otherwise.
Deadpool. Most of the time, he wants to do the right thing... the problem is, he's nuts. He doesn't always have the best judgment on what's right and wrong.
One early appearance of Doctor Strange's extradimensional enemy Dormammu portrayed him this way, with Doc realizing Dormammu did have a bizarre and alien sense of honor which Doc could use to his advantage once he understood it.
Cyttorak, another extradimensional magical god, empowers both the Crimson Bands of Cyttorak, one of Strange's Signature Moves, and The Juggernaut, one of the X-Men's most powerful enemies. Therefore, he provides power to one of the greatest forces for good, and one of the greatest forces for evil, on Earth. Why? Why not?
One of the Eternals books invokes this. It is set after the Super Registration Act is passed, and Iron Man is trying to get them to register, eventually saying that "you must choose a side." The Eternals' leader replies "Imagine that you find two kids fighting over who gets a plastic ball. Would you choose a side?"
Frank of Jim Woodring's eponymous Frank comics, and pretty much all the characters in the Unifactor. Their morality ranges from simple selfishness to extreme sadism, but without any reference to whether it's good or bad. There is some internal consistency for each character's morality, but not between the characters. The lack of words adds to their separation from moral norms.
Galactus was originally intended to be one of these. More recent interpretations have put him more into Above Good and Evil territory, with varying reasons for his planet devouring ways.
The Endless show this at times, and at others are utterly human. Plus, each character's personality lends them different ways of dealing with the world. Dream shows this multiple times, such as not punishing a creature which dominates others' dreams to create a 'nest' because it is simply acting in its own nature. Death never (well, almost never) interferes with the natural demises of anything, no matter how much she likes the individual and Destiny knows when catastrophic events will occur, and will only summon the others for a meeting about said catastrophes if his book says he does.
In general one of the themes of the book is that one is ultimately a a slave to their own nature. The Cuckoo who creates a nest and is harming others is not evil, that is how her species lives. Cain actually loves his brother Abel deep down, but cannot simply stop killing him because if he did not kill his brother he would not be Cain. Morpheus creates and employs nightmares, which by definition are dreams that frighten people, and rewards them for doing so (when one nightmare walks out on his job to become a serial killer, Dream is more annoyed he abandoned his post than anything else). Beings of all kinds can change and grow, but in the end you can only change so much before you become an entirely different person.
The New 52 version of Superboy sometimes has trouble understanding moral issues, as he hasn't really had much time to learn about it. He honestly doesn't understand why robbing a bank gets him complaints.
Atrocitus' moral code is very simple: Killing and destroying whoever or whatever has made you mad. In Supergirl storyline Red Daughter of Krypton Sheko reads his mind and notes that he's a monster by her people's standards, but he's utterly convinced that his actions are righteous and necessary.
Bizarrogirl is not evil. She is... backwards. She rampages through a city and kidnaps a bunch of people because she looks to throw a party, and she shuts her guests up when they try to talk. As she fights alongside Supergirl, she learns morality human and the difference between killing and saving people, remembers she killed a man because he was too loud and has a breakdown.
Dr. Manhattan of Watchmen is above it all. When Ozymandias is asked about Dr Manhattan's political allegiances, he replies, "Which do you prefer, red ants or black ants?" When the reporter admits he has no preference on such a trivial matter, Ozymandias says that Jon has the same opinion about the factions of the Cold War.
Usagi Yojimbo: Jei is a self-described "servant of the Gods" who considers it his task to cleanse the world of "evil". However, how he determines who is "evil" or "innocent" seems completely arbitrary to anyone with anything resembling conventional morality.
Poison Ivy apparently considers killing plants to be just as bad as murder, but thinks actually murdering humans is ok. Good luck figuring that one out.
Harley Quinn in the New 52 is a downplayed example. While most of the things she considers immoral aren't that weird, her reactions are often so violent and over the top it's hard not to find them a bit disturbing. Case in point, in the first issue she sees a guy neglecting his puppy and gets upset enough to take the puppy under her wing and drag the guy behind her motorcycle till she eventually crashes (due to the cops chasing her) and he dies.