The name "Save the cat" for this trope was coined by scriptwriter Blake Snyder, after the scene in Alien in which Ripley saves the cat from the alien.
A quick one for Davy Jones in Pirates of the Caribbean: At World's End: seeing incoming cannon fire, he throws himself on Mercer to protect him from the blast. The fact that he quickly remembers he hates the man and promptly chokes him to death just reinforces the fact that he would have protected any member of his crew in the same way.
Elsa, Indy's Bond Girl and the perfect embodiment of an Aryan antagonist in The Last Crusade, reveals herself to be a villain when she tricks Indy into giving up an important Plot Coupon. She's a Nazi, but she's also a dedicated scholar and archaeologist who earns our sympathy when she weeps at the sight of her countrymen burning books. Doesn't save her from a Karmic Death, mostly because of her being Too Dumb to Live.
In the movie Sin Nombre we see the protagonist bringing a child to be violently initiated into a local gang. So far he seems evil, but he soon pets the dog when he visits his girlfriend, with whom he appears to have a loving relationship.
Face/Off, there's Castor Troy tying his dead brother's shoes; and to a lesser extent, beating up a boyfriend who attempts to rape Archer's daughter.
Another one is a scene after the two stay at the monastery. Tuco leaves after an intense argument over their chosen lives with his brother who became a monk. Tuco is visibly saddened, though upon seeing Blondie he praises his brother greatly and tells him what a great dinner he had. Blondie, being the smarter of the two, is not fooled but he plays the game saying something along the lines that there's nothing like a good smoke after a good meal and offering Tuco one of his trademark cigars. This to a man who wanted to walk him to death through the desert. Eastwood tried to do the same thing to him earlier in the movie for no reason. So its not like he didn't deserve it.
Even a complete sociopath like Angel Eyes can't help but feel sorry for a group of soldiers he passes by that aren't very well off; he bribes one soldier with alcohol for information about Bill Carson and lets him keep it. In a more subtle example, he pays a handicapped man at the second attempt to hang Tuco in coins for some information on Carson earlier in the film.
In the movie The Watcher, Keanu Reeves' character pets a dog. The dog belongs to the women he strangled with piano wire seconds ago. But he's a good guy.
In the very first scene of Beetlejuice, Adam is established as a decent person in an unusual way. A large spider is crawling around his model construction of the local town, so what does Adam do? He gently picks up the spider, remarks on its unusual size, and releases it outside.
The rescued rabbit featured in the 1982 movie Local Hero seemed to exist purely for this purpose.
Captain Von Trapp has many of these moments in The Sound of Music, but most notable is his sudden affection to his children when he returns home, finds his children singing, and suddenly sings with them, and then to them. The Von Trapp children react with shock and/or crying, and at the end of the song, they all embrace him. (Also a Pet the Dog moment for the actor, Christopher Plummer, who didn't like working with children, and distanced himself from them. Allegedly, the children's reactions were genuine when filming this scene, since it gave them the feeling that he actually liked them.)
At the end of Dogville, after Grace has her mob associates kill every man, woman and child in town, she specifically tells them not to kill a dog.
Made of Honor does this several times over, to show that the protagonist isn't a total asshole. He even kisses the dog.
The TV movie A Is for Acid featured mass murderer John Haigh adopting a dog, taking good care of it, and breaking down in tears when it finally died. The reason the dog needed adopting in the first place was that he killed its owners and dumped them in a vat of acid to cover it up, but there you go.
The main villain in Vantage Point amasses a rather large list of crimes over the course of the few hours in which the movie takes place, including killing many civilians, is unable to run over a little girl, ultimately proving to be his undoing - his van crashes and he is caught.
In Duel, the villainous truck driver rescues a broken down school bus between attempts to kill the man who dared to pass him on the road. It seems there's some very laser guided road rage at work.
Literal example: Frost/Nixon has the defeated and broken ex-President pet a dachshund after admitting his guilt in the Watergate scandal. Nixon was the avowed master of dog-petting. (See Real-Life examples, below.)
The Nome King in Return to Oz actually comforts a crying Dorothy, and offers her a way to rescue the Scarecrow- which quickly transforms into a deathtrap as he transforms from an Elemental Embodiment to a particularly vile near-human. Whether or not the King's sympathy was ever genuine is up for debate.
Further, after all the other members of Dorothy's group have entered the Death Trap and she's awaiting her turn, the Nome King even offers to send her back to Kansas, albeit without changing her friends back. This all might have more to do with the King being Affably Evil rather then genuine kindness on his part. Again, a matter of debate.
Nastily subverted in Schindler's List. Amon Goeth seems intrigued by the concept of showing occasional mercy, and waves off a concentration camp inmate with "I pardon you." He then repeats the phrase to a mirror... which is followed by him sniping the "pardoned" man from his balcony.
And again when he gently caresses his Jewish paramour, only to immediately begin beating her savagely.
In the Lethal Weapon series, Riggs starts out as a borderline Ax-Crazykilling machine. Then, after slaughtering his way through the first two films, he refuses point blank to kill a guard dog. Instead he makes friends with it (by sharing his dog biscuits), then steals it. He was already on his way to being a nicer guy, but this was the proof that he was now just a slightly wacky cop (with a two-digit body count).
Near the end of The Departed, Colin Sullivan attempts to pet a neighbor's dog in the hallway of his apartment building, but the dog shies away.
October Sky has a classic example: Homer Hickham's father stops yelling at his son briefly to go rescue his son's friend, who is being beaten by his drunken stepfather. After threatening him and sending him on his way, Hickham comes right back and continues to yell at Homer, proving that he is a good man.
In The Fly 2 (the sequel to the Cronenberg movie starring Jeff Goldblum), the mutated insectoid protagonist happens to pet a golden retriever in the lab shortly before going on a revenge spree against the apparent bad guys of the film, making us (ostensibly) root for the monster in the film, for once.
West Side Story has a subtle example. During the Jets' opening dance-march through their territory, while making it very clear how they consider themselves the de facto owners of this chunk of the city, they pointedly walk around a little girl's chalk circle rather than interrupt her.
The 2004 German film Downfall features the last days of Adolf Hitler's bunker. While not denying his fundamental insanity and monstrosity, it not only features him petting his dog but also showing other moments of (relative) humanity. This might count as a subversion, as they go more towards why people followed him despite the fact that he actually WAS a monster.
In the film The Usual Suspects, Michael McManus pats an, understandably, concerned-looking canine as he makes his way through the drug runners' boat, cheerfully murdering the Hungarian smugglers in cold blood.
There's also a literal example earlier on in the film when a few of Willard's men open fire on a boat of civilians believed to be running supplies for the NVA. It turns out that they were innocent but they do happen to find an adorable puppy that Lance proceeds to stroke and take with him.
The Big Bad of Man on Fire is a kidnapper who is shown covering and caressing his own children while negotiating the ransom of his victims.
In Snow White: A Tale of Terror, the wicked stepmother goes right ahead and murders her brother, leaves her stepdaughter lost in the woods while trying to magically kill her, poisons the entire castle and enslaves them magically, seduces her stepdaughter's fiance, and rapes and nearly murders her husband. During the big fight between her and the stepdaughter, she completely ignores her opponent when she hears her baby son crying, running to tend to him despite the fact that the stepdaughter is armed and more than ready to press any advantages.
She was also a sympathetic character in the beginning of the movie, trying to reach out to her stepdaughter, who acts like a brat to her. It's only when she miscarries her own child that she snaps.
"On second thought, drinks are only half off." (pause) "On second thought, double the price of everything."
Child's Play. As Ax-Crazy as she is, Tiffany seems to love Chucky in her own crazy way and genuinely seems to care about their child later on, even before learning that he/she is their kid. When she dies, she even warns him/her to not make the same mistakes she and Chucky did.
Half of The Invisible is this. When we meet Annie Newton, she's an coldblooded thief and gang leader, which is all the protagonist Nick thought she was, especially after she beats the tar out of him and leaves him for dead. He is very disturbed when he sees how much she cares for her little brother.
Nick: Stop acting like you're a person!
Pando in the film Two Hands is a ruthless Affably Evil (emphasis on "Evil") crime boss who would have no qualms about murdering you if you cross him... but he very clearly loves his young son and is very close to him, in one scene watching Play School with him and complimenting the origami pterodactyl he made. A major theme in the movie is that even bad people have some good inside them and vice versa.
In Snatch, the ruthless gangster Bullet Tooth Tony, who has no problem whatsoever shooting, slicing or otherwise dishing out pain to human opponents, in one scene balks at Avi's suggestion to "open" the dog in order to obtain the massive diamond which said dog had swallowed.
In one of the deleted scenes in 15 Minutes, the main bad guy Emil Slovak is shown helping an old lady across the street.
While the Red Queen in Tim Burton's Alice in Wonderland is more than ready to cut the heads off of anyone who crosses her and uses cute animals for furniture, she still has a vulnerable moment in which she confides to the Jack of Hearts that she wonders whether it is indeed better to be feared than loved and tells him that she's happy that he at least cares for her (the fact that he doesn't makes him quite the bastard). She later is more than happy to befriend the very tall Alice and keep her as a "favorite" (granted, she doesn't know it's Alice, but she does feel sorry when the girl says she was kicked out of her home town for being too large).
Near the end of Oldboy, the villain Lee Woo-jin has a pet the dog moment where he for Oh Dae-su after he drives the man past his Despair Event Horizon. Woo-jin had a trap set up to destroy Dae-su and his lover completely, where he would reveal to both that they are father and daughter. After Dae-su's horrifying breakdown (during which Woo-jin laughs hysterically), he seems to pity him and calls his associate, telling him not to go through with the rest of the plan.
Crash is heavily devoted to showing jerks petting the dog. One that stands out in particular is near the very end of the movie, when a carjacker who had been preaching racial pride, intolerance and selfishness throughout the film finds himself in possession of a van filled with smuggled Asian slaves. When he's offered a good deal of money for them, he instead takes them to L.A.'s Chinatown and frees them, giving one of them forty dollars to buy them some food.
Another notable one is when the Middle Eastern shopkeeper blames a locksmith for his shop being broken into and robbed (the locksmith was not at fault, but the shopkeeper was paranoid from racial persecution). When the shopkeeper goes to get the money back, he holds the locksmith at gunpoint and accidentally shoots the locksmith's young daughter, which horrifies him. When she isn't hurt at all, he sees it as a sign from God, decides that the girl was sent to show him to get his life back on track, and gives the gun to his daughter. His daughter actually loaded the gun with blanks, but he never realizes this.
In Star Wars: Return of the Jedi, after Luke kills the rancor (the murderous creature Jabba the Hutt tries to feed him to), its keeper emerges from the shadows, shouting in alarm, and begins sobbing when he sees that his pet is dead — giving a touch of humanity to one of Jabba's evil flunkies. The Expanded Universe later defined him as a Gentle Giant who hated Jabba for mistreating the rancor, and eventually gave him a happy ending after Jabba's death.
Played rather hilariously in The Young Philadelphians: Tony isn't a monster, but he's straying dangerously close to Amoral Attorney territory. When an elderly lady comes to his office wanting to write her chihuahua into her will, he seems disinterested and rather annoyed when the dog starts walking around on his desk...but when he makes a phone call and learns that she's ridiculously wealthy and influential, he immediately scoops up the dog and begins cuddling it. Made all the more delightful because it's Paul Newman.
Played straight in American Gangster: Frank Lucas is a ruthless African-American mobster who has no qualms about setting people on fire, shooting someone in the head, in broad daylight, on a public street, or flooding the neighborhood with heroin that leaves mothers too wasted to even take care of their children. Yet, he is a family man who cares for the poor and uses his personal wealth to bring both his family and his city up out of despair, and when caught, he (arguably) goes way overboard in bringing both mobsters and corrupt policemen to justice. One scene in particular - Lucas handing out turkeys to impoverished Harlem families - is a perfect example of this trope.
In Captain America: The First Avenger, the film manages to give The Red Skull such a moment with a self serving caveat. This is when The Skull is about to board his rocket chopper and tells Dr. Zola that the ride's only for himself. Instead of abandoning him to Captain America, the Skull gives Dr. Zola the keys to his Cool Car to make his own escape with instructions that it must be not be damaged in any way. This means that the Doctor will be delivering his car to the rendezvous point instead of being confiscated by the Allies.
The primary role of Robert in Mystery Team up until The Reveal, with him agreeing to take care of the children he had accidentally orphaned
Mini from Mini's First Time is about as close to soulless as it is possible to portray in film, but even she gets a little Pet the Dog moment: when some guy at school is teasing her friend Sprague, Mini defends her. Given the way in which she defends Sprague, and her overall character, it is possible that she only does it for her own amusement, and not out of any care she might have for another person.
In Scarface, Tony Montana provides the most violent example of this trope ever by blowing the head off someone that deliberately tried to murder a mother and her children right before said person is about to push the button. This shows that Tony still has some good in him, though this act also causes the falling-out with Sosa which ultimately leads to Tony's death.
In Tim Burton's Sleepy Hollow, the Horseman is shown to be very affectionate toward his steed. In the flashback that shows his origins, he is shown petting the horse as it lay dying from a gunshot wound, and toward the end the Horseman is happily reunited with it once he gets his head back and drags Lady Van Tassel down to hell with he and his horse.
The RiffTrax for Spider-Man 3 commented — "See, this just goes to show that Spidey cannot, and will not, kill this guy. I mean, imagine how different Star Wars would have been if the first scene had shown Darth Vader stroking a puppy."
In Tinker, Tailor, Soldier, Spy, a major Pet the Dog moment is actually pretty suspicious: a British secret agent, Jim Prideaux, is shot and captured by the Soviets, but after his interrogation he's sent home in one piece. This implies that The Mole had sympathies with Prideaux, and pulled strings to make sure he lived. It's no reflection on Prideaux's loyalty - the mole is Bill Haydon, who, despite his treachery, is extremely close to Prideaux and never intended for him to get captured.
The only living thing that Alex of A Clockwork Orange shows any concern for is his pet boa constrictor, Basil. When Alex comes home after after serving two years in prison, he's upset to learn that Basil died during this time, supposedly from an accident.
In The Third Man, 'Baron' Kurtz petting a dog while trying to confuse Holly Martins.
In The Jackie Robinson Story, the title character takes a cat away from some racists who are trying to intimidate him by mistreating the cat
Subverted in The Cabin in the Woods. Hadley, one of the engineers behind the massacre at the cabin, remarks that he's actually rooting for Dana to make it out alive ... only to lose all interest in her struggle with a zombie when he sees some party guests bringing tequila into the room.
The Godfather has an almost-literal example in the very first scene. The eponymous mafia overlord tenderly plays with a cat while hearing an assassination request. A Throw It In by Marlon Brando, who made friends with that cat on the street and insisted they work it into the scene. It's the rare case where a Right-Hand Cat is actually used to humanize its master.
Towards the end of Thirteen Days, John F. Kennedy is in a meeting with the military and is being urged to attack a SAM site that shot down one of their planes. Kennedy wants to wait and make sure it wasn't an accident. The Chiefs are about to protest, but Gen. Curtis LeMay , who up to that point had been the biggest General Ripper of the lot, sides with Kennedy. He has a practical reason for doing so, but it shows he's not so eager for Commie blood that he'll just rush into a fight.
Mr. Wint: How kind of you, Mr. Kidd. The children will be so thrilled.
In Les Miserables (2012), Javert, when looking through the bodies of the revolutionaries, finds the corpse of Gavroche, the young boy who recognized him as a mole and almost got him killed. Javert takes off one of his medals and pins it on the body.
Despite being an abusive husband to Victoria and a self-destructive asshole in general, Oliver Thompson from My Letter To George shows genuine sorrow when their baby is stillborn.
In RoboCop (1987), the remorseless mobster Clarence Boddicker finds his assassination mark in the company of two hookers and deigns to shoo them away rather than killing them as witnesses.
In The Room, Johnny - gradually established an almost a Messianic Archetype of general niceness - famously stops to pet a small pug belonging o the owner of the flower shop, despite everyone in the scene seeming incredibly rushed.