Not to mention both pre-timeskip Lord Genome and the Anti-Spiral, who, despite being mortal enemies, are both using the same basic strategy of tyranny to protect what they love (humanity from the Anti-Spiral for Lord Genome, the universe from humanity for the Anti-Spiral).
With a few exceptions, this trope is all over the Gundam franchise.
One good example in Gundam SEED is when Mu La Flaga, resident Ace Pilot and Big Brother Mentor actually expresses some sympathy for Omnicidal ManiacRau Le Creuset. It's worth noting that La Flaga is the only person in the whole series who seems to understand Le Creuset's motivations, let alone sympathise with him, while still of course, agreeing that he needs to be stopped. Sharing the same Abusive Dad may have helped.
Similarly, Black Lagoon is full of sympathetic devils. The only exceptions that come to mind are the Neo-Nazis (who are misguided and comical) and Chaka.
Rave Master Haru Glory has been sympathetic towards several of his foes upon learning the events that brought them where they are. However, his first experience with this through King taught Haru that despite his sympathy "We have to fight anyone who inflicts pain upon the innocent. That's the path we've chosen."
Nearly does in Robin Mask when he faces Kinnikuman Mariposa in Kinnikuman's Scramble for the Throne arc. Mariposa tells Robin about his past, in which he was forced into thievery due to poverty and Robin, who had never faced a foe with a Tragic Past before, couldn't bring himself to pile more defeat onto Mariposa. It took a reminder that Kinnikuman himself was a bigger Butt Monkey than Mariposa ever was and overcame it without falling to evil before Robin could get back into the fight guilt-free.
In the anime version of Sailor Moon (it's last season, Stars, to be exact) All the Sailor Senshi (yes, even Uranus and Neptune) shed tears after learning about Nehellenia's Start of Darkness. It was hard for them to imagine living with the sadness and loneliness she endured. This prompted Sailor Moon to return Nehellenia to her childhood, giving her a second chance at life.
Johan Faust VIII from Shaman King is first presented as a ruthless, cruel, and slightly insane antagonist. He gets a fair bit of sympathy when it's revealed that his fairytale romance with his wife Eliza was cut short like an ironic Greek tragedy, leaving him a broken man. Anna actually recruits him as the team medic in exchange for Anna summoning Eliza's spirit. Having his beloved wife back mellows him out to the point that he's a valued teammate, if still crazy.
In Death Note, after shooting and almost killing Light, Matsuda is shown to feel a degree of pity for him, as does Aizawa in the anime (ironically, he tells Matsuda he shouldn't feel pity for Light in the manga). In the spin-off manga chapter starring Near, Matsuda does freely admit though that Light was "an evil person".
One episode of Cowboy Bebop has this as it's title. The devil turns out to be a boy whose aging process was halted by the explosion of a hyper-space gate prototypenote He killed a lot of people to keep up the masquerade..
Yuu from Holyland comes to realise that some of the gangsters he comes into conflict with just want a place they can call their own, just like him. The main difference is that he's content to defend what he can get, while they are aggressive and expansionist in doing so.
This appears to be the ultimate Aesop for the anime version of Blue Exorcist; have sympathy for demons, and try to understand them before you try to destroy them. Rin and Yukio's mother, Yuri, literally had sympathy for Satan himself.
When Aizen is finally defeated in Bleach, Ichigo is only able to feel pity for him after sensing the soul-crushing loneliness that ultimately drove Aizen's delusions of godhood.
In Tokyo Mew Mew, the Mew Mews learn that their enemies once lived on earth, but were forced to leave when the environment shifted, taking refuge on a world that was inhospitable. They returned, only to find that the humans are polluting it, and seek to kill all the humans and reclaim Earth. Zakuro says it's understandable that they would be upset over what is happening to what was once their planet, but points out that it doesn't justify their crimes.
Blood+'s Saya Otonashi shows pity/sympathy for Diva for her tragic Freudian Excuse several times in the series, although it doesn't stop her from carrying out her duty when Diva threatens her family and the world. When she finally succeeds at killing Diva, Saya holds her and cries for her as she dies.
Jonathan Joestar in Part I of Jojos Bizarre Adventure had every reason to hate Dio Brando. Despite everything, he still shed tears when he apparently defeated Dio. Even after Dio mortally wounded him, Jonathan's last act was to embrace Dio's head, acknowledging that he still considered Dio his brother.
Naruto: Naruto despises Obito for his Straw Nihilist views, but as he works to finally separate him from the tailed beasts, all of his emotions and memories come flooding in with them. Naruto experiences visions of the man's past, his dreams of becoming Hokage, his mourning Rin's death, and is genuinely moved to tears over Obito's loss.
The Electric Tale of Pikachu: After the Black Fog chooses to self-destruct rather than let Ash capture it, Sabrina sheds tears for it, remarking that even though she's hated the Black Fog for years for killing all of her Pokemon, she just can't help but feel sorry for it.
In Nanatsu No Taizai, King sympathizes with Helbram despite the latter doing all sorts of atrocious things. This is because Helbram is actually King's old friend who had gone mad with hatred for humans due to King being too late to save him.
Elfen Lied: Even though Lucy killed his father and little sister in a jealous rage, Kouta, despite openly admitting that he can't forgive her actions, can't actually bring himself to hate Lucy herself no matter what and would rather get her to stop killing than seek revenge.
In Scott Pilgrim, this is materialized as the Power of Understanding.
The DCU: First shown in Neil Gaiman's The Sandman and then later confirmed in his own title, Lucifer, the Prince of Hell, is actually not that bad a guy once you get to know him. Sure, he's bitter about how God's treated him over the last several billion years, he's arrogant, he's a bit of an asshole, but he's not the soul-stealer Christianity and Islam would have you believe he was.
In the Buffy comic series Tales of the Vampires, a group of young Watchers-in-training are brought before a captured vampire who tells them all about vampires both as monsters and people. At the end, after foiling an attempt by this vampire's sire to free him, (and killing the sire) the main character acknowledges that she did learn from the vampire and apologizes for his loss as he weeps disconsolately.
In the Sonic the Hedgehog comic series, Sonic is shown to feel visible guilt when a series of defeats reduces Dr. Eggman to an insane babbling wreck. Granted this comes to an end when he regains his stability, and all his ruthlessness and more, shortly afterwards.
Likewise, when Fiona starts crying and denying that she trusts and depends on Scourge, Sonic just walks away with a pitying look on his face, muttering, "Keep telling yourself that."
The Legend of Spyro: A New Dawn: Despite everything she's done, Spyro and Cynder remain sympathetic to Deadlock, stating that the circumstances that drove her insane could have easily broken anyone.
In the MLP fanfic What Have You Done and the sequel Even As.., Twilight sees Discord as just like her, another abandoned creature after she crosses the Despair Event Horizon when she is alienated from her friends and family due to the Canterlot Wedding. She decides that Discord does not deserve being in stone, and uses a stone reversal spell to set him free.
The Twilight Child: Even after all she's done to them, the Cutie Mark Crusaders try to reach out to Diamond Tiara after she's been on the receiving end of a "The Reason You Suck" Speech. Diamond Tiara's response is to scream and swear at them until they go away.
Film - Animated
In Kung Fu Panda, Master Shifu faces Tai Lung when the latter makes his way to the Jade Palace. During their battle, Tai Lung angrily calls out Shifu for pushing him to train so hard his bones cracked, filling his head with dreams of becoming the Dragon Warrior, and turning his back on him when Oogway denied him the Dragon Scroll. Exhausted and beaten physically and emotionally, Shifu acknowledges the part he played in Tai Lung's descent and apologizes for failing him. Unfortunately, Tai Lung just wants the Scroll.
In Kung Fu Panda 2, Po pities Shen and tries to help him. This is pretty damn impressive considering that it happens after Po learned that Shen slaughtered damn near his entire race, including his mother.
It's brief but in Rise of the Guardians, the Guardians all wore an expression of pity when Jamie runs right through Pitch, indicating that the Boogie Man is no longer feared or believed in.
In Brick, the Pin, a club-footed drug dealer barely out of high school, briefly opens up to the hard-boiled hero on the beach. Talking about his love for Tolkien, he reveals himself as something of a sad, lonely geek.
Will Graham: This started from an abused kid, a battered infant... My heart bleeds for him, as a child. Someone took a kid and manufactured a monster. At the same time, as an adult, he's irredeemable. He butchers whole families to pursue trivial fantasies. As an adult, someone should blow the sick fuck out of his socks. Does that sound like a contradiction to you, Jack? Does this kind of thinking make you uncomfortable?
Raoul Silva in Skyfall. During his confrontation with M where he reveals his Tragic Villain backstory, when he says "You betrayed me," Bond looks away from Silva and gazes intently at M. After Silva has a mini-meltdown where he reveals his cyanide-induced deformity (for which he also blames M), M leaves and Bond turns to follow, but slowly and hesitantly, suggesting he doesn't entirely want to leave Silva alone. After he rejoins M, he stares silently at her until she explains why she "betrayed" Silva. According to Daniel Craig on the DVD special features, under better circumstances Bond would have rather let Silva live and get therapy.
M, for her part, is visibly shaken after Silva's big reveal and her explanation is tinged with melancholy. Later in the film, as they are lying in wait for Silva's final attack, she says, "I fucked this up, didn't I?" While Bond assures her she was just doing her job, he doesn't go so far as to tell her she did the right thing.
Several characters for Gollum. In The Hobbit, Bilbo has pity on him and doesn't kill him when he has a chance, despite Gollum trying to kill and eat Bilbo. Frodo and Sam, who initially feel no pity, both develop compassion for Gollum after they've experienced the burden of bearing the Ring and are able to imagine what five hundred years of that would do to a person. Especially poignant with Sam, who's spent most of the book (understandably) regarding Gollum as a vile, treacherous little creature who deserves no sympathy.
Aziraphale and Crowley in Good Omens, quite cordial for an angel and a demon (specifically, the angel with the flaming sword who guarded the gate of Eden and the demon who took the form of a snake and tempted Eve).
Possibly best summed up in this exchange:
Aziraphale: "I'd just like to say, if we don't get out of this, that ... I'll have known, deep down inside, that there was a spark of goodness in you."
Crowley: "That's right, make my day."
Aziraphale: "Nice knowing you."
Crowley: "Here's to next time. And ... Aziraphale?"
Crowley: "Just remember I'll have known that, deep down inside, you were just enough of a bastard to be worth liking."
Erast Fandorin and Momos in The Jack of Spades (Special Assignments) by Boris Akunin.
He's also the inspiration for Rolling Stones song mentioned in the Trope description
A version of this occurs in Raymond E. Feist's The Riftwar Cycle. The dark elves of the setting, also known as moredhel or the Brotherhood of the Dark Path, are generally portrayed as evil and sadistic, with no morals and a love of torturing their victims before killing them. A huge invasion by the moredhel and their allies is the main plot of one book, A Darkness At Sethanon. In spite of that, the Big Bad of that book, the charismatic moredhel leader Murmandamus, is revealed to be a Pantathian (snake-person) priest in disguise who doesn't care about the moredhel and only wants the Lifestone below the city of Sethanon, an artifact that supposedly has the power to revive the Pantathians' Valheru mistress and revered goddess. On top of it all, the power to use said Lifestone comes from the life forces of all the people who died near the priest, the bulk of which is moredhel soldiers who died in a careless siege against a very well-defended fortress, thus making the moredhel the ones who were most cruelly used and manipulated, resulting in literal Sympathy For The Devil, or for the Dark Elf at least.
On top of that, two other books - Krondor: The Betrayal, which deals with events ten years after the invasion, and Honored Enemy, which is set before the invasion - feature moredhel protagonists and switches to moredhel perspective for a change, also making them a bit more complex and multi-faceted rather than the standard 'evil and sadistic' image. Additionally, in Feist's universe dark elves are really the same as light elves, just with a different culture, as opposed to being a different race, as in many other settings.
The Incarnations of Immortality novel "For the Love of Evil" tells the events of the previous six books, all from Satan's point of view. It definitely plays this trope well, showing both how Parry became Satan through evil he performed, how effectively he evokes evil (it is his job) yet how, secretly, is actually a very good man.
Both in-story and out-of-story with Mayella Ewell, "the loneliest person in the world," in To Kill a Mockingbird. This is particularly true if you happen to catch one easy-to-miss remark, spoilered here because it has the most impact in context: "She said she never kissed a man before, and she might as well kiss a nigger. She said what her pa do to her don't count." Also, she pretty much has to raise her family by herself, and she has no idea what a friend is. She has a few plants that she takes care of, and that's pretty much the only thing of hers. It's really pretty sad.
A quite literal sympathy in the case of Hand of Mercy - the Fallen are are depicted as a small band of martyrs just trying to end their people's slavery.
I, Lucifer literally has Lucifer attempting to create sympathy or rather simply telling his side of events. He largely succeeds in both regards. He also mentions the trope naming track, The Rolling Stones' "Sympathy For The Devil".
While learning about Voldemort's Back Story, Harry expresses a twinge of sympathy when Dumbledore reveals that his mother chose to die in childbirth, rather than save her life with magic and raise him alone.
Harry's hatred for Draco is replaced with pity after the events of Book 6. He even saves Draco's life in the last book and Narcissa repays the favor.
In Warrior Cats, when the villain Tigerstar is killed, Firestar reflects on the fact that normally he'd be relieved or happy that this dangerous cat is gone, but all he feels staring down at Tigerstar's body is grief. Tigerstar had been gifted with strength, intelligence, and charisma, and he could have become a legend as one of the greatest warriors in history had he not chosen to follow a dark path.
In It, this is one of the reasons why Mike can't quite bring himself to kill Henry Bowers in self-defense. Mike pities him for having grown up under someone like Butch Bowers, who naturally heavily influenced Henry's way of thinking and was partially responsible for his son's racism and jerkassery.
In Undead on Arrival, Novak spends the entire book hating and hunting down his killer, only to discover it's a poor kid who regrets what he did.
In Season 5 of Supernatural Lucifer tries this multiple times; with Sam at the beginning of the season after appearing as Jess, Sam's dead girlfriend, with Dean when Zachariah sends him into the future, and with Castiel in "Abandon All Hope", while he has Cas trapped in a ring of holy fire. Subverted in that none of these attempts work. Dean even references the trope when calling Lucifer out on his "Sympathy for the Devil crap".
Scorpius of Farscape fits this trope very well. He pursues Crichton throughout the second season for his knowledge of how to use wormholes. By the end of the third season however, Crichton genuinely considers giving it to him when he comes to understand Scorpius' motivations, though in the end he chooses not to.
24: In Season 7, Jack and Renee corner Tony Almeida just as he is about to kill Alan Wilson one of the major figures responsible for killing David Palmer, Michelle Dessler, and her and Tony's unborn son. They are both forced to shoot him to save Wilson. However, both of them clearly heard Tony crying about his unborn son beforehand. As the FBI agents take Tony away, he yells at Jack in anger and berates him for letting the bad guys get to this point. While Jack's reaction to the whole thing is hard to tell (at least partially because he is severely suffering from the pathogen weapon infection and is close to death at this time), Renee is clearly saddened and utterly horrified. She further demonstrates these feelings when she bitterly tells Wilson that she blames him for Larry Moss's death, even though Tony was the one who actually killed Larry as part of his cover to gain Wilson's trust.
Once Upon a Time loves this trope. The series started with two delicious baddies in the Evil Queen/Regina and Rumplestiltskin/Mr Gold. Then we found out that Rumpel turned dark because he took the power of the Dark One in order to save his thirteen-year-old son from being sent to certain death fighting in the Ogre War. That dark power twisted him into the ruthless (though not completely irredeemable) Dark One. But we still have the evil Queen, until we find out she was stuck in a miserable marriage with Snow White's father, after her mother Cora murdered her beloved because he was only a stable boy and she wanted her daughter to be queen and that Regina hates Snow White because as a child Snow inadvertently caused the murder of Regina's beloved by telling Cora that Regina was going to run away with him. Then there is Cora who seems like a wonderfully wicked and remorseless villain until we learn she truly loves her daughter and acted as she did because she grew up a poor and hardworking miller's daughter who was treated like dirt by the royalty until she finally vowed she would get her revenge by becoming one of them and making them all bow to her and her child. As Rumpel says "Evil isn't born, it's made."
In Dino Attack RPG, after the Darkitect's Divine Intervention granted Dr. Rex a Fate Worse than Death, many Dino Attack agents felt pity towards Dr. Rex. Even Rex, who moments prior proclaimed that Dr. Rex deserved to die a slow and painful death, realized that no one, not even Dr. Rex, deserved the terrible fate he met.
Brikman Mc Studz: "As I was reading that post, I felt just a very small shred of sympathy for Dr. Rex. Sympathy best described using a quote from a review by Roger Ebert for the movie Der Untergang (Downfall) to describe sympathy toward Hitler in the film: "Sympathy I felt in the sense that I would feel it for a rabid dog, while accepting that it must be destroyed."
Although this was averted in the final game, Metal Gear Solid 4: Guns of the Patriots, where Old Snake is too tired to give a crap. Drebin instead fills him in the Beauty and the Beast Unit's backstories if he defeats them non-lethally, relating the emotionally-scarring situations that made them the way they were. Snake actually tells Drebin once that he doesn't care about such ridiculous sob stories, but Drebin keeps talking anyway.
Played straight with Rose, however, who finds said backstories absolutely heartbreaking; she even states that Liquid is truly a heartless monster for forcing such broken people to fight, remarking that they'll eventually break down and be completely useless. Snake agrees with her on all points, but also points out that, since they're nuts and thus not fighting at their full effectiveness, he has an advantage.
Priestess Meden and General Gong Hawkeye of Patapon. Gong's your enemy, yes, but - all things considered - he's also a likeable fellow who certainly strikes a chord with Meden. He tries reasoning with you before he goes to battle, he mourns his fallen comrades, he tries to prevent Queen Karma from selling her soul to the demons and in the end he faces your army alone in a heroic last stand. It's very cruel that you have to kill him to progress in the game.
Ganondorf: My country lay within a vast desert. When the sun rose into the sky, a burning wind punished my lands, searing the world. And when the moon climbed into the dark of night, a frigid gale pierced our homes. No matter when it came, the wind carried the same thing... Death. But the winds that blew across the green fields of Hyrule brought something other than suffering and ruin. I... coveted that wind, I suppose...
Link and Zelda show pity for the alternate timeline version of Ganondorf, in The Legend of Zelda: Twilight Princess after his death, which is somewhat strange given how this Ganondorf is portrayed. While we know from Wind Waker that both final versions of Ganondorf were originally out to save his people, this version never regains his sanity and remains a Big Bad, despite similar circumstances of imprisonment. Needless to say, he's not intended to be sympathetic.
After Link apparently kills Ganondorf in The Legend of Zelda: Ocarina of Time, Zelda says he was a pitiful man who could not control the power of the gods and met an ignoble end as a result.
In the original Shadow Hearts, as Yuri and the party find out more about Roger Bacon's imposter, Albert Simon, they start to feel this way towards him. The final battle with him is as rivals deciding the course the world should take, rather than a showdown between Good and Evil... and when he loses, he uses the last of his power before dying to send Yuri and his friends to destroy the Meta God, keeping his word that, win or lose, both sides would accept the consequences and there would be no hard feelings.
The sequel takes it even further, with most of the antagonists being at least somewhat sympathetic. The Final Boss, in fact, could probably have finished his plans without interference if he hadn't told Yuri and company when and where to meet him.
At the end of Mother 3, where Dr. Andonuts traps Porky inside the Absolutely Safe Chamber, he notes that for all the horrible things he's done Porky was deep down an insecure and lonely little boy driven by the fact that everybody hated him.
That last one wasn't helped by him being a Jerkass since early childhood. While it explains the reason behind his actions, it hardly justifies them to any extent.
Well, he tries to do this with Xemnas when he seems to die the first time but then Xemnas comes back to screw him and Riku over again. In this light, his previous attitude was probably more justified.
Master Xehanort, the Big Bad from Birth By Sleep, is quite skilled at exploiting this trope, even if he doesn't deserve it. He tricks Terra into listening to him not by pretending to be a good person, but by admitting to doing horrific things to Ven and then feigning guilt to earn Terra's pity. Unfortunately for Terra, it works all too well - it's all too clear that he really does feel sympathy for Xehanort, and trusts him more than he should because of it.
In Icewind Dale2, the spirit of Mother Egenia and Iselore are the only characters who express sympathy for the Big Bads Isair and Madae. Egenia was the one who raised the twin cambions after their birth mother was Driven to Suicide. Her spirit mourns her children's turn to darkness but recognizes that they have to be stopped. Iselore was the one who named the twins when they were born. He recalls with shame his warning to Egenia that "they are forged in evil and nothing but evil can come from them!" and wonders if this was a Self-Fulfilling Prophecy.
Most of Altair's targets get this treatment. So do a surprisingly large number of Ezio's.
In Dissidia: Final Fantasy, upon defeating Kefka for the final time, Terra feels that his urge to destroy was because he was incapable of finding anything to live for save for destruction and that he was trying to find something to fill his "broken heart".
Many of the chosen of Cosmos appear to feel this way towards their designated foes. The Warrior of Light openly admitted feeling pity towards Garland. Zidane never stopped reaching out to Kuja. And despite his claims of hating his fathers guts, Tidus once gave Jecht a potion so they could fight on equal terms. In fact, it might be easier to list off the number of heroes who don't feel some form of sympathy for the villains.
In Ace Attorney Investigations, Kay feels some pity for Shih-na/Calisto Yew, who killed her father, because she believes that she was able to look into her heart while speaking to her, and she wonders what it would be like to do all the terrible things she did without feeling anything.
In Devil May Cry 3, Arkham manages to use his status as Lady's father to manipulate her into moving into the place he needs her. He tries it again before the final battle when he's kicked out of the demon world by not being able to handle Sparda's power. He's near death at this point, so he loses and lets it slip that he saw absolutely nothing wrong with killing his wife to become part demon. Lady finally has enough. At the same time, Dante obviously feels similar about Vergil since the two are brothers. He doesn't feel good about having to fight him but has to due to Vergil's ambitions being dangerous towards humanity. He even cries for a moment when he meets back up with Lady.
Elvis in God Hand. He's implied to eat people, yet what we see is an overall nice guy who punishes his men for disrespecting the dead and has a lot of similarities to Gene. Gene even says they could have been friends if he were human. When Shannon insults him later after his death, Gene makes her pay.
Viola in Zone of the Enders. Even Dingo seems to have a lot of respect for her in the sequel although he's fighting a CPU copy of her. She died at Leo's hands.
When talking to the Big Bad in the final route of Duel Savior Destiny before he unveils himself, Taiga finds himself sympathizing strongly with the man. He realizes that he himself could have easily become quite twisted if he had undergone the same situation.
In Nier, Popola and Devola reveal themselves to be soulless artificial humans and the closest thing the game has to a Big Bad and fight you. Things take a tragic turn when Devola is slain. Popola is distraught because she can't bear to be alone. Nier pauses and begs her to stop fighting. Popolasnaps, claiming there's no way she can stop after her own sister was cut down in front of her. The boss fight then continues, the action packed boss theme of the first round of the fight replaced with a tragic reprise.
In Assassin's Creed III, the Templars are given several sympathetic motivations for their plans and have justification unlike the previous games were they simple said they had the moral high ground, but simply used the order to gain more power. In almost all of their death scenes they come across more as AntiVillains than anything else.Considering the ending and what we know happen in the history books it may give you the feeling that it would've been better for them to succeed. It's even sadder when you find out that the Templars, just like the Assassins, were more or less Unwitting Pawns of Juno, the true villain of the series, manipulated into fighting a meaningless war.
By the end of Heaven's Feel, Shirou realizes that he no longer hates Kotomine. He actually kind of likes him. In fact, he's more similar to Kotomine than to his own hero figure, Kiritsugu. In the end, there's only a fight to the death because Kotomine is following his 'ideal'/way of living to the end, and Shirou just wants to save his Dark Magical Girlfriend Sakura. Saving the world is a perk. Kind of sucks that he was born so broken.
In season 10 of Red vs. Blue, the Reds and Blues spend the entire season trying to take down the Director and even fight an army of Tex robots to get to him. When Carolina and Church finally reach him, however, Carolina finds him so broken and miserable that she can't bring herself to kill him. This may have more to do with him being a terrible father and her allowing herself to let go of her own demons than actually granting him mercy, but it is certainly an example of this when he asks her to leave him her pistol and she does so with barely a word.
Ben 10: Ultimate Alien: In the episode "The Enemy of My Frenemy," Charmcaster sacrifices 600,000 people, including Ben, Gwen, and Kevin, to bring her Disappeared Dad back to life. However, her father can't bear to be the cause of so many deaths and thus dies to bring all those Charmcaster sacrificed back to life. Charmcaster is so heartbroken over this that Ben and co. agree not to arrest her for her actions out of pity.
In The Legend of Korra, after hearing Tarrlok and Amon / Noatak's backstory Korra says that it's one of the saddest stories she has ever heard. In season two, Korra is the only one who feels bad about not being able to stop Unalaq without killing him. Unalaq was such a terrible person that even his own children don't regret his death.
In Thundercats 2011, the Lizards are actually given an understandable motive for siding with Mumm-Ra. Under the reign of the Cats' kingdom Thundera, most of the arable and prosperous lands are controlled by the Cats while the other species are left to starve and are often captured and enslaved if they try to steal food for their people. This is explicitly stated by a Lizard who was captured and tormented by the Cats to Lion-O, which caused him to later defend the Lizards from an angry lynch mob.
Batman is certainly capable of empathising with adversaries with more tragic backstories, though he doesn't let it stop him from preventing their schemes if they are endangering the lives of others. This is most notable when he sees a recording of what happened to Victor Fries and his wife.
It's telling that, especially compared to his more campy or Darker and Edgier incarnations, this Batman actually does seem to want to reform his Rogues Gallery rather than simply beat them down over and over, displaying a heavy amount of this trope. That's why Joker tweaks him so bad; rather than having a tragic backstory (Mr. Freeze, Poison Ivy) or being legitimately, untreatably insane (Firefly, Riddler and his obsessiveness), the Joker seemed to be in complete control of his faculties and just saw the world as a big playground and every other person was simply a cheap toy to be played with and discarded. For him, the only one who was really a devil didn't deserve any sympathy, and yet he still gave it whenever possible.
In Trial, it was outright stated that Batman and most of his Rogues Gallery were most likely Not So Different: Deeply troubled individuals who reacted to great hardship by putting on a mask and lashing out. The big difference being that Batman put on his mask and lashed out against crime, while the villains put on a mask and lashed out at society.
Mostly subverted by the main heroes in The Dreamstone, there is very little to sympathise about Zordrak, and his minions the Urpneys, though far more sympathetic, are dealt with indiscriminately. Spildit however, naively converses and even attempts to help Sgt Blob's team at times. At one point they even sympathise with each other after Urpgor once again chews the squad out and steals Spildit's leaf.
Spildit: It was very mean of him to take my leaf!
Nug: He's like that sometimes.
In Wakfu, Yugo cannot bring himself to finish off Nox after he sees Nox shedding tears after his plan to Set Right What Once Went Wrong ended in utter failure and allows the defeated villain to leave peacefully. Averted in season two; Yugo feels no sympathy for Qilby the Traitor after hearing his twisted reasons for destroying worlds to fuel his own selfish desires and imprisons him in an empty void. Played straight again in the manga, when Yugo admits that he feels guilty that he left Qilby to that horrible (though justified) fate.