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Tear Jerker: In Bruges
Pretty much all of the movie that isn't comedy qualifies for this. It doesn't help that Ray is suicidal and Ken has to kill him.
The scene in the park, where Ray finally breaks down about killing a little boy and cries into Ken's chest.
Ken's actions for the second half of the movie. Not only does he essentially give the finger to his boss whom he owes greatly, but he spares Ray to the point of taking two bullets and dying for him.
Most of Ken and Harry's scenes carry a sense of sadness; not only do they act like old friends despite Harry arriving to kill Ken, the two are visibly reluctant when they struggle with one another, with Harry even apologizes to Ken when he shoots him fatally.
They even manage this when they're not in the same room; when they have their phone conversation, it starts off hilariously as Ken tries to fake the fact that Ray is already at the pub... and then Harry starts referring to Ray in the past tense. You can see Ken's world start to shatter at that point.
"I went to the park so she wouldn't have to clean it up."
Harry killing himself. Foul-mouthed and violent as he might be, the fact that he earlier said he would do this in the right circumstances and then follows through on his word, with a devastated expression as he says "Oh...I see..." Roger Ebert said it best: "[this event] shows that even professional murderers have their feelings."