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Tear Jerker: Black Lagoon
The end credits music, at least until the very end.
The deaths of Hansel and Gretel. Since the series usually consist of over the top action scenes where dozens of Mooks are gunned down by our heroic sociopath "heroes" without a second thought, an arc that could actually be taken seriously was a severe case of Mood Whiplash. The arc following it was so over the top ridiculous that it actually seemed like an apology to the viewer for putting them through that.
The worst part? That was about as close to a happy ending as they could get. The only way to improve it would be for Hansel's death to have been less painful. That is how screwed up these two were. They are little kids.
Worse still, the ending of the Tokyo arc, the deaths of Yukio Washimine and Ginji Matsuzaki, and Rock's apparent realization that he's one of the bad guys now.
The omake that features Yukio and her classmate Maki can come off as this, especially after the major Downer Ending.
That arc also gives us Balalaika's Start of Darkness. It's especially poignant when you realize that the song playing while Balalaika decides to join the Mafia is the same song that played during Hansel and Gretel's death scenes.
And it's not just the ending or Balalaika's backstory. There's also the scene with Yukio telling her kouhai Maki good-bye and asking her to take care of her mother before she abandons her school and takes over the clan, leaving the poor girl in tears and screaming "Sempai, sempai!"... *SOB*
Revy's face when Rock tells her that despite what she thinks (that he's a normal person who could go back to a normal life) that he's just as messed up as her and right where he belongs. It's like she can't tell if she should smile or cry.
YMMY, but at the end of Roberta's long arc, it's very sad to see all those genuinely decent soldiers get brutally murdered by her, when they were just following orders. This troper lost all hope for Roberta at that point.
This is anime only, but at the end of Roberta's Blood Trail, upon seeing the Nigh InvulnerableNinja Maidreduced to a half-blind wheelchair-bound cripple with one arm and leg missing one can't help but feel a little sad.
Near the end of the Hansel and Gretel arc, Gretel tells Rock what she and Hansel went through, relaying her bleak, nihilistic philosophy about life and the world. Absolutely horrified, Rock gives her a hug and tells her that the world can be a beautiful place and should be a beautiful place, especially for children like her. Unfortunately, having had her humanity stripped from her at such a young age, Gretel doesn't respond in the most healthy of manners. Given how disturbingly common Hansel and Gretel's situation was in Ceaușescu's Romania, it made even this most jaded troper feel something in his eye.
During the Lock-and-Load Revolution arc, after a particularly over-the-top car chase/shoot-out full of snarky back-talk between Revy and Shenhua, sudden Mood Whiplash:
Takenaka: "Ibrahim! Don't forget we have a job to do! IBRAHIM! No matter what you do, or how hard you fight, your son is never coming back!"
The last third of episode 15. Oh God. Also, Episode 24, though maybe not as much.
"DON'T LOOK AT HER, ROCK! LOOK AT ME!" (Rock doesn't)