Dragon Ball, Goku begins the final phase of almost every battle by offering his opponent "one last chance" to recant his evil ways.
At the end of Dragon Ball Z, before annihilating Buu with the Spirit Bomb, Goku briefly reminisces about the events of the arc, and how Buu went from an mostly-innocent manchild to a ruthless killer after losing the battle against his inner evil, and says how Buu will now learn what it's like to have his own life taken away against his will. He also makes a wish that Buu will come back as a better person, so he can fight him again.
Judai/Jaden on loves these, usually couching them in terms of "the true meaning of the game". His opponents hardly ever buy it. Someone always lampshades: i.e. "You know Jaden — he loves giving this speech."
At one point, he decides the speech won't do anything, so he just goes straight to the asskicking.
Mahou Sensei Negima!: Chamo and several others comment on this, stating that Negi would end his fights a hell of a lot quicker if he wasn't holding back so much at the start of major fights, trying to give his opponent a chance to surrender. They never do.
During the Mahora Festival arc Negi decides that he doesn't know whether the Big Bad's plan (ending The Masquerade) is the right thing to do or not. He fights them anyway because they can't prove that ending the Masquerade is important enough to justify screwing over Negi, his students, and the other mages.
The King in The Law of Ueki delivers one of these to Margaret, and the entire race of Protectorates. Nobody listens.
In Digimon Adventure, Angemon and Angewomon make absolutely sure that Myotismon has no remorse for any of his evil deeds before killing him.
Naruto: Naruto does this to a lot of villians, from Haku to Gaara to Kurama, the Nine-Tailed Demon Fox. Part of the story's Aesop relies on this trope. The belief of his sensei, Jiraiya, was that there will come a time that "people truly understand each other". However, the entire shinobi world is built and perpetuated on a never ending Cycle of Revenge. During Naruto's fight with Pain, Pain questions if Naruto thinks that killing him, and thus continuing the cycle, will make things better. Naruto's answer to this is to listen to Pain's story, tell him why his Evil Plan is flawed and that that's a better way. Pain realizes that he's a Fallen Hero, and then immediately switches to Naruto's side.
In Pokťmon Special, this is what Dia does to every villain he's ever encountered before resorting to fighting them. It may not work for the villain, but it sure does inspire everyone else who hears it (even Dialga and Palkia, in one instance!).
Magic Knight Rayearth: Umi gives one to Fluffy Tamer Ascot when he tries to yell at her for killing his "friends." After an Armor-Piercing Slap, she points out that he is the one forcing them to fight the trio and doing so will make people more fearful of them than they already are. It works so well that he does a Heel-Face Turn and shows up in Part II by using his creatures to help the remnants of Cephiro's population... and he has a huge crush on her.
In the climax of Superman: Brainiac, Superman gives Brainiac one of these during their final fight on Brainiac's skull ship:
Brainiac: I hold life in the palm of my hand. I control life.
Superman: Life can't be controlled. Life can't be bottled. All this knowledge, and you don't know anything about life. This ship isn't life, Brainiac. This ship is your bottle. And I'm going to take you out of it.
He then blasts Brainiac through the wall of the ship, where he lands in an Earth swamp and immediately freaks out at the contact with its myriad micro-organisms.
Moka: You kidnap and brainwash our friend, you sent Kuyou down upon us, you used us like toys... all so you can destroy the world with Alucard? All I see before me is a misguided fool that is going to be cast down into Hell.
Films — Animated
Po of Kung Fu Panda does this in both movies. He tells Tai Lung why Tai wasn't ready to have the Dragon Scroll, and tells Shen to let go of the past. Neither works in the slightest, showing that the villains are beyond redemption.
In The LEGO Movie, Emmet appeals to Lord Business' hidden insecurity by reminding him that people have been inspired by his creations to build their own, signalling his redemption. This is paralleled in the real world, where The Man Upstairs apologises to his son after becoming impressed with the latter's creations, both mirrors hugging it out. The lid is put back on the glue, and the world is saved.
Megatron: Is the future of our race not worth a single human life? Optimus Prime: You'll never stop at one.
In X-Men, Magneto tells our heroes (whom he has handily all bound up with metal) his plan. Wolverine calls him out.
Wolverine: You're so full of shit. If you were really so righteous, it'd be you in that thing.
Flipped in Serenity: The Anti-Villain tries presenting this trope to the Anti-Hero, who in turn delivers the Shut Up, Kirk! by shooting him. The villain then stands up (not being an idiot, he saw that coming and wore body armor) and resumes.
Labyrinth played it as a key plot point, as it was her destiny to deliver her "Give me the child" speech. Foreshadowed and all.
In Star Trek: Nemesis Jean-Luc Picard delivers a Kirk Summation to a hologram of his clone, Shinzon, in his ready room during a lull in a space battle, appealing to his better nature. Shinzon goes for genocide anyway.
Slightly inverted in War Of The Gargantuas through the monsters themselves. Sanda tries to "talk" (through gestures) to his brother, Gaira not for them to fight. Gaira however, being a more wild and savage clone of his brother doesn't listen and continues provoking Sanda to fight, which they ultimately do, to the death.
In Man of Steel, Zod begs Superman not to destroy his ship, saying without it, Krypton cannot be restored. Superman says, "Krypton had its chance!" and destroys it.
Thor gives Loki one during their climactic final battle.
Harry Potter vs. Voldemort, round 4. Harry calls him "Riddle" and suggests he repent, before summarizing: "So it all comes down to this, doesn't it? Does the wand in your hand know its last master was Disarmed? Because if it does... I am the true master of the Elder Wand."
Not a villainous example, but Wedge Antilles, on a world of Proud Warrior Race Humans, repeatedly hints at his disgust for a moral system that revolves around killing for honor. The native fighter acting as his guide falls for him, sees that she has no chance, and tries to go through honorable suicide-through-combat. He stops her when he sees what she's doing, and they have an exchange where he tries to convince her not only to stay alive, but to see and move past the flaws in her culture's beliefs.
Wedge: Circular thinking. I'm honorable because I kill the enemy, and I kill the enemy for the honor. There's nothing there, Cheriss. Here's the truth: I kill the enemy so someone, somewhere — probably someone I've never met and never will meet — will be happy. [...] I told you how I lost my parents. Nothing I ever do can make up for that loss. But if I put myself in the way of people just as bad as the ones who killed my family, if I burn them down, then someone else they would have hurt gets to stay happy. That's the only honorable thing about my profession. It's not the killing. It's making the galaxy a little better.
High-King Kallor of the Malazan Book of the Fallen once boasted to Caladan Brood of the many kingdoms he had raised, ruled, and then destroyed. He asked if Caladan could understand what that meant. And Caldan calmly replied "Yes. You never learn."
Faith: Oh yeah? Give me the speech again, please. "Faith, we're still your friends. We can help you. It's not too late." Willow: It's way too late. You know, it didn't have to be this way. But you made your choice. I know you had a tough life. I know that some people think you had a lot of bad breaks. Well, boo hoo. Poor you.
Buffy tended to come across this trope whenever there was a recurring villain, or a Face-Heel Turn, either subverting it or playing it straight at random. In a later season, Anya lampshades the arbitrariness of the gang's mercy ("Spike has some sort of get out of jail free card that doesn't apply to the rest of us...").
Doctor Who also featured quite a few of these. They would frequently add a twist wherein the villain actually would be persuaded by the speech, then be promptly killed by his even more villainous Lieutenant. In the later years, they became more cynical about this — the seventh Doctor used these speeches in Silver Nemesis and Remembrance of the Daleks, knowing they would only goad the villain into carrying out his plan without taking the time to notice the Doctor's sabotage.
Possibly the Doctor's defining Kirk Summation occurred in Colony in Space:
The Master: The point is that one must rule or serve - that's a basic law of life! Why do you hesitate, Doctor? Surely it's not loyalty to the Time Lords, who exiled you on one insignificant planet?
The Doctor: You'll never understand, will you? I want to see the universe, not rule it.
Doctor Who also featured a full-out subversion in "The Christmas Invasion", where the Doctor gets halfway through a speech before realizing that he's just been reciting the opening lines of "Circle of Life" from The Lion King.
For the Tenth Doctor in particular, this was a defining part of his much more pacifistic character — the villain was always given a chance to repent, usually followed by "or else, I'll have to stop you." The "a chance" part is quite specific, too. They get exactly one chance. They aren't told what will happen if they don't take it, but they learn the hard way that the Doc does not play around.
This is arguably overused in the RTD era to the point that in episodes like Rose and The Poison Sky people die because the Doctor insists on giving the villains a chance that he should know they won't take. In the latter, he keeps on trying to convince the Sontarans to leave even when they've turned him down flat.
In the Series 4 finale, Martha Jones even goes against her UNIT orders, to give the Daleks the chance to stop because "there's one more thing the Doctor would do."
"I'm so old now. I used to have so much mercy. You get one warning. That was it." in "School Reunion" sums it up perfectly.
"No second chances. I'm that sort of a man."
The Tomorrow People manages a few, notably when the Tomorrow People debate the values of their version of history with the representatives of a 20th century Roman Empire:
Gaius: How can one man rule unless others obey? How can one be free without slaves?
Elizabeth: How can any man rule wisely without first learning to obey? How can any man be free while others are enslaved? How can anyone achieve greatness while others are prevented from fulfilment?
She possibly tops that when she dismisses Colonel Masters' claim that weaponising telepaths will put an end to war, pointing out that's what people have thought about every new weapon:
They even thought that the old English longbow would put an end to war, after the carnage it caused at the Battle of Agincourt. Well, there've been a few wars since Agincourt, haven't there, Colonel?
The turning point in the main arc of Babylon 5 hinges on a Kirk Summation that actually works. Kirk Summations also appear at other points in the series and often work, most notably during the early stages of the Earth Alliance civil war.
In the series finale of 24 when Jack Bauer becomes a tragic Villain Protagonist in his quest to seek revenge against the one who's screwed him over for the last time, Chloe desperately tries to keep him from ultimately going through with it, as she's even reluctantly holding a team of agents on stand by to come in and take him down if she ultimately fails. She also happens to remind Jack that said person he's trying to kill is the head of the Russian government which will lead to Russia declaring war on the United States if he's assassinated and that the person he's trying to avenge would never want him doing anything like this. It ultimately works.
In Tensou Sentai Goseiger in the final battle, the Goseiger calls out Brajira on why is he trying to destroy the Earth when he is a Gosei Angel himself:
Alata: Brajira! Why do you want to destroy the Earth so badly?! You are a life-form who was born of this Earth too!
Agri: Yeah. You grew up on Earth like us!
Moune: We receive our power from Earth. That's why we are alive!
Hyde: Just what do you think your power exists for?!
Eri: Doesn't it protect Earth and all life on it?!
Yggdrassil: Why can you not accept the ideal world that I have created? Lloyd: How can your world be ideal when you've caused countless innocent people to suffer? Yggdrassil: Human. Don't tell me what's right and wrong.
Used in Mass Effect where Commander Shepard may attempt to convince Saren that Sovereign is controlling him through his cybernetic implants, and that they can still defeat the Reapers. Depending on your alignment, you can either convince Saren to kill himself, or suggest that he can make a Heel-Face Turn and redeem himself. Unfortunately, however Saren dies, Sovereign assumes direct control of his corpse, making you have to kill the guy TWICE, rather than just once.
Also used in Mass Effect 3, where Commander Shepard may attempt to convince The Illusive Man that he is being controlled byTheReapers through his cybernetic implants, and that he can redeem himself if he makes a Heel-Face Turn. Shepard must have played the game consistently as a Paragon for this ploy to work, otherwise he must shoot The Illusive Man before The Illusive Man executes both Anderson and Shepard. Fortunately, when The Illusive Man dies, he stays dead, leaving Shepard to activate the Crucible and defeat the Reapers.
She may not be the lead character of the series, but Luna Platz pulls one of these on Tia's little brother, even telling his alien partner Corvus to shut it when he tells her that he just wants to cause random destruction.
In World of Warcraft, Tirion Fordring gives a Kirk Summation to the Lich King several times, including during the Argent Tournament and during the final fight with him in Icecrown Citadel. In ICC, Tirion offers a swift death for the thousands the Lich King has tortured and slain. The Lich King responds with a Breaking Speech, to which Tirion replies Shut Up, Hannibal! and shortly frozen in ice and taken out of the fight.
At the end of Wrathion's questline in Pandaria he begins ranting about how Wrynn threw away a golden opportunity when he didn't use the Siege of Orgrimmar as an opportunity to subjugate the Horde. The previously silent innkeeper then berates Wrathion for completely missing the lessons of Pandaria: It is the conflict between opposites that makes them stronger; destroying one will weaken the other. Wrathion calls him an innkeeper and leaves in a huff.
The most prominent example of this in Duel Savior Destiny are attempts on Rubinas' part to talk down Lobelia, who is so bitter and resentful that she completely refuses to believe anything about how her friends valued her. When Rubinas points out that Lobelia was never resented for her abilities or appearance, she is instead met with claims of betrayal.
Delivered in The Salvation War by Michael to Yahweh at the beginning of his coup attempt, though it's from a villain, albeit an Anti-Villain at this point, rather than a hero.
Coop's "three things that annoyed me today" speech in almost every episode of Megas XLR, although it's always said before the villain gets trashed, and just as easily subverted (such as him blaming an enemy for things that weren't their fault, often Coop's fault instead) or said by other characters (including the villain in one episode). Lampshaded during an Enemy Mine scenario:
Coop: All right, squid. You tried to wreck the city again, made me go to some alternate dimension where Jamie is a bigger creep than usual, and you got me locked up in a jail with no food?! It's time to rumble! Gorrath: Are you talking to me? I'm on your side now, remember?! Coop: Oh, sorry. Force of habit I guess.
After Joe McCarthy had tried to bully and bluster his way through hundreds of hearings, destroying hundreds of lives in the process, Joseph N. Welch was having absolutely none of that shit. His famous line "have you no sense of decency sir" is only the end of an epic and righteous speech:
"Until this moment, Senator, I think I have never really gauged your cruelty or your recklessness. Fred Fisher is a young man who went to the Harvard Law School and came into my firm and is starting what looks to be a brilliant career with us. Little did I dream you could be so reckless and so cruel as to do an injury to that lad. It is true he is still with Hale and Dorr. It is true that he will continue to be with Hale and Dorr. It is, I regret to say, equally true that I fear he shall always bear a scar needlessly inflicted by you. If it were in my power to forgive you for your reckless cruelty I would do so. I like to think I am a gentle man but your forgiveness will have to come from someone other than me...Let us not assassinate this lad further, Senator. You've done enough. Have you no sense of decency, sir? At long last, have you left no sense of decency?"