The Schofield Kid's moment of clarity in Unforgiven, which comes in two parts in one scene, a set-up and payoff:

THE KID: Say, Bill...
MUNNY: Yeah.
THE KID: That was... the first one.
MUNNY: First one what?
THE KID: First one I ever killed.
MUNNY: Yeah?
THE KID: How I said I shot five men... it wasn't true.
(long pause)
That Mexican... the one that come at me with a knife... I busted his leg with a shovel... I didn't shoot him or nothin'.
MUNNY: Well, that fella today, you shot him alright.
THE KID: (forced bravado) H-hell yeah. I killed the hell out of him... three shots... he was takin' a sh-sh-shit an'... an'...
The Kid is shaking, becoming hysterical, he can't go on, and Munny hands the bottle back.
MUNNY:Take a drink, Kid.
THE KID: (breaking down, crying) Oh Ch-ch-christ... it don't... it don't seem... real... How he's... DEAD... how he ain't gonna breathe no more... n-n-never. Or the other one neither... On account of... of just... pullin' a trigger.
MUNNY:It's a hell of a thing, ain't it, killin' a man. You take everythin' he's got... an' everythin' he's ever gonna have...
THE KID: (trying to pull himself together) Well, I gu-guess they had it... comin'.
MUNNY: We all got it comin', Kid.

Then, a little later at the end of the scene:

MUNNY: Lemmee see that Schofield, Kid.
THE KID: Wha... what f-for?
MUNNY: (sharply) Lemmee see it.
THE KID: Sure. Sure, Bill.
Munny takes the pistol and begins to check it methodically, inspecting the load first... and The Kid watches nervously, shifting from foot to foot.
THE KID: You... you could keep it, Bill. I ain't... gonna use it no more, I ain't gonna kill nobody. I... I ain't like you, Bill.

http://www.youtube.com/watch?v=XoAPKt7kbD0

Breakthrough therapy scene in Good Will Hunting:
http://www.imdb.com/title/tt0119217/quotes?qt0408086

Funny you used "On the Waterfront" because it definitely was in Stallone's mind when writing Rocky.

The moment similar to "I could've been a contenda'" is "If I can go the 15 rounds with Creed and be standing there when that bell rings, only then, I'll finally know that I'm not just another bum from the street." (quoted from memory...may not be totally right)

In a way, he updated it to "I AM a contenda'"

Pulp Fiction!

Jules: There's a passage I got memorized. Ezekiel 25:17. "The path of the righteous man is beset on all sides by the inequities of the selfish and the tyranny of evil men. Blessed is he who, in the name of charity and good will, shepherds the weak through the valley of the darkness, for he is truly his brother's keeper and the finder of lost children. And I will strike down upon thee with great vengeance and furious anger those who attempt to poison and destroy My brothers. And you will know I am the Lord when I lay My vengeance upon you." Now, I been sayin' that shit for years. And if you heard it, it meant your ass. I never gave it much thought. I just thought it was some cold-blooded shit to say to a motherfucker before I popped a cap in his ass. But I saw some shit this mornin' made me think twice. See, now I'm thinking, maybe it means you're the evil man. And I'm the righteous man. And Mr. 9mm here, he's the shepherd protecting my righteous ass in the valley of darkness. Or it could mean you're the righteous man and I'm the shepherd and it's the world that's evil and selfish. And I'd like that. But that shit ain't the truth. The truth is you're the weak. And I'm the tyranny of evil men. But I'm tryin', Ringo. I'm tryin' real hard to be the shepherd.

http://www.youtube.com/watch?v=vMN5uQhF-Ro (audio's a little low on this clip. Could also use a deeplink to a longer clip: http://www.youtube.com/watch?v=fMRi-gFeK-M#t=6m0s)

Thanks, Scott - I'm honored! And I've got one last line from PENN AND TELLER GET KILLED.

Penn: Thanks. You've kept me alive and taught me a very important lesson: One should never go on national TV and beg psychopaths to kill one.