Battle Royale: Antagonist girl gets ambushed by the psycho who volunteered and is shot after a brief struggle. Keeps getting up and knocked down by each consecutive gunshot until she just collapses. *Cue J.S. Bach - Air on the G string*
Epitaph: "I Just didn't want to be a loser anymore". Girl #11 Mitsuko - Dead. 7 to go.
Gattaca: The very end. Cutting between the engines igniting as Vincent takes off into space, and Jerome puts on his second-place swimming medal as he
climbs into the incinerator.
"For someone who was never meant for this world, I must confess I'm suddenly having a hard time leaving it. Of course, they say every atom in our bodies was once part of a star. Maybe I'm not leaving... maybe I'm going home."
12 Monkeys: Cole is in the car and just breaks into tears upon hearing "Blueberry Hill" played on the radio as he tries to sing along. Either that, or the end.
Magnolia: The whole last hour.
Ran: (quoted from an imdb user comment) "There is one scene that struck me as remarkable, and then for the rest of the film I couldn't take my eyes off of Nakadai whenever he was on screen... It involves the first battle sequence, in which one of his son's comes to take over a castle, and killing all of Hidetora's men. Look at Nakadai in the scene where he's sitting down stone-faced amid the chaos going on outside, and then as he somehow manages to walk out, the fellow soldiers making way for him. He then sees one of his sons, the betrayer, and he doesn't say a word- he's already decided that his son Taro has gone too far with his position, as he rules over his domain and scares the peasants right out of the picture- and he simply walks away, as his family continues to crumble under corruption of the mind and heart."
Leon - The Professional: "This is... from Mathilda" *gives grenade pin to Stansfeld*
Hana-Bi: Hard to name any specific scenes. But there are many melancholic scenes related to the central shoot-out, its aftermath, and the inevitability of his wife's condition.
Some other good ones have been mentioned, like the Seven Samurai, the Shawshank Redemption (especially once the old Librarian gets paroled) or Requiem for a Dream.
If it breaks, you get to keep both pieces.