A surprising number of villains feel bad for all the crap the Straw Hats go through in One Piece. It usually helps show the Morality Kitchen Sink going on all over the place. Most notably, Franky, leader of a vicious bounty hunter gang, breaks into tears when he hears how Usopp left the Straw Hats to keep the Going Merry. Keep in mind, he had savagely beaten up Usopp about a dozen chapters ago, and was now holding him prisoner. This eventually leads up to his Heel-Face Turn.
In Naruto, toward the end of Hinata's fight against Neji, Neji's teacher, Might Guy appears slightly sad when noting that Hinata is no longer able to fight against Neji and gives Neji a What the Hell, Hero? when he tries to kill her. Fridge Brilliance kicks in when you remember that he's also Lee's teacher, and he strongly identifies with those who are trying to take down a more talented opponent through hard work and determination.
Saki Achiga-hen, Toki has a moment like this with Kuro, who is beginning to despair when facing the champion, Teru, and is not able to fight back effectively. Toki notes that Kuro, by attracting all the dora tiles, is hindering Teru's ability to make progressively larger hands, and is quite pleased with Kuro when she finally discards a dora tile, enabling her to win off Teru.
During the Kindly Ones volume of The Sandman, Lucifer notes that while he once swore to destroy Dream (over a fairly trivial matter) he now feels almost sorry for him when he sees the mess that Dream has gotten into.
In Captain Atom: Armageddon, Cap gets a lot of this, especially from Mr. Majestic and the Authority, who both recognize that Cap is a good man and a hero, and that it's not his fault that he's going to blow up and destroy the universe. They do their best to help him, and Angie Spica, the Engineer, a member of the Authority, even gets romantically involved with him. That doesn't stop her, and the rest of the Authority, from trying to kill him, in the mistaken belief that that will stop him from destroying the universe.
There's a scene in The Prophecy where Satan briefly commiserates and shows sympathy to Detective Daggett, (a cop who years earlier lost his faith just before he was set to become a Catholic priest) about how hard it is to believe and keep faith.
Villain Protagonist Yuri Orlov shows a grudging respect and admiration for Hero Antagonist Agent Valentine several times in Lord of War. Specifically, Yuri goes out of his way to point out Valentine's honesty and integrity, and Yuri seems to be showing some sympathy when Valentine is about to be betrayed by the system he has risked his life defending.
In the 2003 film version of Peter Pan, Hook uses a Breaking Lecture on Peter to take away Pan's flight and distract him. Throughout it Hook talks about how Wendy will grow up, and move on, leaving Peter to die alone, forgotten, and unloved. At the end he suddenly looks tremendously sad and adds "Just like me".
Spider-Man Trilogy: After Spider-Man saves the train from falling off the tracks in the second film, he's exhausted and almost falls off the train. The people in the train pull him back in and lay him on the floor. Peter's lost his mask in the fight, so everyone in the train can see how young he is. One man notes with sympathy "He's... just a kid. No older than my son." One young bystander gives Peter back his mask, and they promise to keep his secret. Then when Doctor Octopus returns, they all vow to protect him. Unfortunately Doc Ock doesn't have a problem with that. The first movie also has Innocent Bystanders coming to Spidey's aid when he chooses to save both MJ and the children, enabling him to succeed and disproving, at least for the moment, the Green Goblin's claim that eventually the people will come to hate him.
The Joker often tries to relate to Batman throughout the course of The Dark Knight, especially in expressing how they're both freaks on the margin of society. At the very end he even grudgingly praises the fact that Batman is incorruptible, and cannot be made to break his moral laws.
At the very end of The German, The German silently offers a cigarette to Red Leader, after both pilots have been interned by the neutral Irish.
This is the source of Riddick's redemption in Pitch Black. He's a borderline sociopathic murderer who has been killing people all his life to escape his past and will sacrifice anyone to save himself. Carolyn Fry starts out much the same way; while not being a criminal she's willing to jettison all the passengers in the opening and tries to cope with the guilt for the rest of the movie. Riddick initially admires Fry for her "strong survival instinct" and offers her at the end to leave the planet together by threatening to leave her behind to die if she doesn't. She eventually refuses and professes her willingness to die for the others. This declared intent of self-sacrifice intrigues Riddick enough to go back with her.
The Night Flier: Despite being a mass-murdering monster, the vampire Dwight Renfield has some respect for Richard Dees, the reporter who's investigating his feedings. He sees Dees as something of a kindred spirit, and goes out of his way to get him to stop pursuing death so he doesn't have to kill him.
Jaime Lannister expresses sympathy for how Ned's older brother and father were executed, believing it heinous. He muses over the fact it was the Starks cruel treatment at the Mad Kings hand that was one of the reasons why he killed Aerys and yet such an act brought him the contempt of Ned Stark.
In The Bible, Pontius Pilate only reluctantly allows Jesus' execution, acknowledging that he had done no wrong by Roman laws. This has carried over to numerous portrayals of Pilate.
In Gor book Outlaw of Gor, when Tarl returns to Gor he finds that his city has been reduced to rubble by the Priest-Kings, and a mind-altered representative of the Priest-Kings shows up to inform him that it's all Tarl's fault. But Tarl sees that the man who is being used as a puppet by the Priest-Kings is crying for him - he feels pity for Tarl, the one emotion that's forbidden in Gorean custom.
In the novelization of the Mortal Kombat movie, Goro sadly tells Johnny Cage's friend Art that Art fought well just before killing him at Shang Tsung's command.
Live Action TV
In the Hornblower episode Duty, Wolfe states that he sincerely admires Commander Hornblower. It's just that he hates everything that he stands for.
In one The X-Files episode that takes place in a carnival, a member of the freak show wonders how Mulder can bear to be so perfectly normal in appearance.
Despite working for Yggdrasil corporation in their behind the scenes manipulation in Kamen Rider Gaim DJ Sagara seems to genuinely respect the determination and resolve of the Beat Riders in general and Kouta in particular.
Game of Thrones has Varys, like his book counterpart, express sympathy for Ned Stark. He notes he almost forgets that there genuinely noble people like him in the world. However he then notes how the Crapsack World of Westeros treats them and why good people like him are so rare in the first place.
Jaime Lannister expresses a degree of sympathy and respect for Ned Stark despite their being no love lost between them.
Tyrion Lannister as well expresses sympathy towards the Starks, Sansa in particular since she's the captive of his family.
On Arrow, Slade expresses this towards Moira, who sacrifices her life during a Sadistic Choice directed towards Oliver so that both of her children get to live.
This was the central idea for the song Superman by Five For Fighting. John Ondrasik said the inspiration was thinking about how Superman is missing out on living because of his Chronic Hero Syndrome.
In Cyrano de Bergerac, De Guiche, initially a villainous character, comes to feel great respect for Cyrano. He recognizes that Cyrano doesn't prosper because he never sacrifices his principles, and he (De Guiche) lives a life of prosperity because he does, and part of him wishes he had Cyrano's moral courage.
In Antony And Cleopatra, Octavius Caesar spends most of the play bringing Antony down, but still seems to feel sorry for him; though the "Poor Antony" line can come across as either sincere or mocking depending on the direction, his open and indisputable grief when he hears of Antony's death suggests he was sincere.
Mass Effect 1 and Mass Effect 3 with Saren and The Illusive Man, both stating "It's too late for me." The latter more poignant when he says, "Your idealism is... admirable."
Several of these show up in endings from the Samurai Shodown series. For example, in the second game Haohmaru's ending has his murderous rival Genjuro acknowledging the grueling fight Haohmaru had been through and being talked into sparing Haohmaru's life by Haohmaru's Love Interest, Oshizu. Later, after Haohmaru parts from Oshizu to continue Walking the Earth, Ineffectual Sympathetic Villain Gen-an, a goblin creature, says that the parting moves him to tears.