Mal's choice to disguise Serenity as a Reaver vessel is also treated as a Shoot the Dog - he is desecrating the corpses of their deceased friends and turning their home into an abomination in order to defeat the Alliance.
In I Am Legend, Neville hauls his dog (and only living/sane companion) Sam, who had been mauled fending off the infected to his secret base, injected her with the only experimental cure that had even begun to show results, and hugged her. Then, as the hair loss and aggression became undeniable, he snapped the dog's neck. Cue Heroic BSOD.
The same thing happens in the Vincent Price version.
Full Metal Jacket, at the very end, when Joker delivers the Coup de Grāce to a downed Vietcong sniper who had shot two men down from said platoon and proceeded to torture them with more shots to their limbs to entice more of the platoon to enter the killzone to save them. She was also a teenage girl. The rest of the platoon wanted to let her slowly bleed to death, but Joker gave her a Mercy Kill.
At the end of Road to Perdition, Tom Hanks shoots Jude Law so that his son will be able to go through life having never killed anyone. In the original graphic novel, his son is the one who pulls the trigger.
In the previous scene, Tom Hanks guns down his father-figure and mentor Rooney (played by Paul Newman) because it is the only way to reach Rooney's Ax-Crazy son and avenge his dead wife and son. Hanks' character is visibly torn apart by killing Rooney, but has no choice at this point.
Sunshine (2007). After a fight with a fellow crewmember and an Important Haircut, Mace becomes determined to focus entirely on completing the mission (which, to be fair, involves saving the entire human race). He first wants to ignore the Distress Call from Icarus Iwhich turns out to be the far better thing to have done, and later volunteers to execute Trey so as to preserve what's left of their oxygen supply. Trey, as it turns out, is already dead.
In X-Men: The Last Stand, when Jean Grey has completely lost control of her alternate personality "The Phoenix", Wolverine is the only one with the fortitude (both moral and physical) to put her down in the end, despite being in love with her. To take the edge off the trope, she regains enough control to request that he kill her. In the original comic saga, Wolverine pointedly can't bring himself to do it.
Done in The Sand Pebbles by Jake Holman (Steve McQueen). After Po-han is captured and is being tortured, the San Pablo is leaving the dock where Po-han is being tortured. Holman is ordered not to fire at the Chinese who are torturing Po-han, so Holman shoots Po-han to put him out of his misery.
Subverted in Zombieland. Wichita asks Tallahassee and Columbus to perform a mercy killing on her "infected" sister, Little Rock, when she stops them, and insists that she be the one to do the deed. She then promptly turns the gun on the two men so that she and her sister can steal their weapons and vehicle.
The Assassination of Richard Nixon: This trope happens near the end of the movie involving Sam Bicke(Sean Penn).
The Fly 2: When Martin (Brundlefly's son) had to put a mutated golden retriever in horrible pain out of its misery by suffocating it with chloroform, after his employer promised him he put it down two years ago. Most gut-wretching scene ever.
In The Warlords, Jet Li is a general whose army has been laying siege to a well fortified town for over a year with neither side making any progress. The Empress tires of the stalemate and has given him a deadline of a few more days. His supplies are running out, and so is the food supply of the besieged town. Both armies are about to starve to death. Li's second in command negotiates a truce with the town's leader, and they agree to surrender the town to Li's army on the condition that they share their food with his people. Li however did not authorize this agreement and afterwards arrives at the cold reality that there is only enough food for his own army to survive for a few more days; were he to share that food with the enemy's troops, neither army would survive. He reluctantly orders the massacre of the entire town that had just surrendered to him. Unarmed, they are all shot down in a hail of arrows. Li's supplies were enough to sustain his army long enough to reach the next town.
The Guns of Navarone. Captain Mallory has discovered that Anna is a traitor and is forced by the circumstances to execute her. As he prepares to do so, Anna's friend Maria shoots her instead so Mallory doesn't have to.
One of the alternate endings for Se7en had Somerset shooting John Doe for killing Mills' wife so that Mills won't have to go to jail for it.
633Squadron. Norwegian resistance leader Lieutenant Erik Bergman has been captured and taken to the local Gestapo HQ for torture and interrogation, so RAF Wing Commander Roy Grant goes over and delivers a precision strike with a single Mosquito, both to silence Bergman and to put an end to the torture.
In 2010's The Expendables, Barney is forced to kill Gunner when he goes rogue in a drug-induced homicidal rampage. Averted when it is revealed in the end that it was merely a Disney Death.
The 1989 John Woo movie The Killer is all about this trope, almost painfully so.
Averted in Shoot 'em Up, where Clive Owen's Mr Smith refuses to shoot an Alsatian to cover his escape, because he likes dogs.
In Fresh (1994), the title character shoots the dog, when it's clear he won't be able to look after it, after his friend who was taking care of it dies.
Daniel Craig's character in Defiance shoots his horse so that the people in his camp can eat again.
Similarly, in True Grit, Rooster shoots the horse when it is unable to carry on due to exhaustion, and he carries Mattie on foot.
In Lean on Me, many of Joe Clark's actions have some arguable moral ambiguity to them, from chaining and locking school doors (in violation of fire safety rules) on being told that someone from inside the school let an expelled student into the building, to firing a teacher for picking up trash during the school song for which everyone was told not to move.
Joe: I cried "my God, why has thou forsaken me?" and the Lord said "Joe, you're no damn good. No, I mean this! More than you realize, you're no earthly good at all unless you take this opportunity and do whatever you have to." And he didn't say "Joe, be polite".
In Vertical Limit, while trapped in an ice cave on K2, one character murders an injured comrade with a syringe of air, rather than share the drug they need to survive at such a high elevation.
Anakin save Palpatine/ Darth Sidious from Mace Windu, but got Mace killed. He did it because Palpatine knows a way to save Padme from dying, but Palpatine really didn't know how, and he crossed the dark side for nothing.
In Dragonheart, Einon can only be killed if Draco is slain because of their shared heart. Since Draco's half is the one with the lifeforce, Draco is the one who must be struck down. He orders Bowen to kill him, invoking the favor that Bowen offered to him long ago. Bowen initially refuses. When he sees Einon get up again as hateful as ever, he realizes that there will never be peace as long as Einon lives. Ultimately, Bowen slays one more dragon.
In Star Trek: First Contact, Picard chooses to shoot a redshirt dead rather than let him be transformed into a Borg (a combination of mercy kill and preventing the creation of another enemy). He finds himself at the receiving end of some major What the Hell, Hero? criticism as result.