In A Certain Magical Index, Touma Kamijou is fond of summarizing the villain's past and motivation and everything wrong with it before declaring, " I will break your illusion!" and then punching the villain out.
It works so well that he does a Heel≯ace Turn and shows up in Part II by using his creatures to help the remnants of Cephiro's population.
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.
Holyland: Yuu gives one in chapter 176 to counter King's attempt at a "Not So Different" Remark.
It may not work for the villain, but it sure does inspire everyone else who hears it (even Dialga and Palkia, in one instance!).
In Pokémon Adventures, this is what Diamond does to every villain he's ever encountered before resorting to fighting them.
Pain realizes that he's a Fallen Hero, and then immediately switches to Naruto's side. Naruto's answer to this is to listen to Pain's story, tell him why his Evil Plan is flawed and that there's a better way. During Naruto's fight with Pain, Pain questions if Naruto thinks that killing him, and thus continuing the cycle, will make things better. However, the entire shinobi world is built and perpetuated on a never ending Cycle of Revenge. The belief of his sensei, Jiraiya, was that there will come a time that "people truly understand each other".
Part of the story's Aesop relies on this trope.
Naruto does this to a lot of villains, from Haku to Gaara to Kurama, the Nine-Tailed Demon Fox.
In Digimon Adventure, Angemon and Angewomon make absolutely sure that Myotismon has no remorse for any of his evil deeds before killing him.
The King in The Law of Ueki delivers one of these to Margaret, and the entire race of Protectorates.
When Arc Villain Arlong asks why Luffy is willing to risk his life fighting him, Luffy's answer is simple: Luffy gets straight to the point when fighting someone. The anime isn't as clear on this as the manga. Though Zechs may have been faking the whole thing.
Of all people, Heero Yuy delivers one in the final battle of Mobile Suit Gundam Wing, rejecting Zechs's assertion that humans need to be forcibly made to give up war.
In essence it is as follows: No, Light, Kira was not a savior but a mass murder you yourself are not a god but a human on a power trip.
In Death Note Near begins one to stop Light's Motive Rant when he finally has him cornered.
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.
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.
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.
She then opts for unleashing raw firepower on them until they're in no condition to do anything but listen to her.
Lyrical Nanoha: Nanoha does this with all her enemies, which never works for various reasons.
Vash from Trigun sometimes engaged enemies in this because of his aversion to killing.
This happens less often in Season 4, mostly preferring to give his enemies short The Reason You Suck Speeches but he gives a good Friendship Speech / Kirk Summation to DARKNESS).
At one point, he decides the speech won't do anything, so he just goes straight to the asskicking.
"You know Jaden - he loves giving this speech."
Judai/Jaden on loves these, usually couching them in terms of "the true meaning of the game".
He also makes a wish that Buu will come back as a better person, so he can fight him again.
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.
It seldoms goes deeper than that, because he's just a kid at this point.
In Dragon Ball, Goku begins the final phase of almost every battle by offering his opponent "one last chance" to recant his evil ways.