Tear Jerker / Green Lantern

• When the Butcher looks into Atrocitus' mind to find out what makes him angry, we see a flashback him with his daughter, telling her they'll be a family forever, followed by one when the Manhunters attacked.
• Dex-Starr's origin story. In short, Dex-Starr - then known as Dexter - was a regular kitty who was adopted by a kindly old owner, only to have his owner murdered by burglars. Then the police officers inspecting the murder kick Dexter out from his former home, thinking he's a stray that will contaminate the evidence of the crime scene. Then some jerks kidnap him, stuff him in a bag, and prepare to throw him off a bridge to his death for funsies, and would have died if the Red Ring that was attracted to his rage at that moment hadn't saved him. It's hard to not feel bad for all the shit the poor kitty went through.
  I find one who hurt you. I kill. I good kitty.^note If it makes you feel any better, Word of God says the skulls that can vaguely be seen next to where Dexter/Dex-Starr is are of his owner's murderer and the two assholes who threw Dexter in the water, so that's not him saying he will avenge her death, it's him saying he did avenge her death and got his revenge. Which is at least something.
• Also, the aftermath of the death of Mogo.
• The death of Sayd. As she holds off the Third Army alone, she pleads to the fleeing Lanterns to tell Ganthet she loved him. Thankfully, she and Ganthet are reunited and happy in the end.
• Hal Jordan's Heroic Sacrifice at the end of Final Night, which effectively ended his era as Parallax. Although it was ultimately temporary (and later revealed to have not entirely been his fault), watching him try to sort out how his life turned out so badly before trying to settle his affairs with those who were closest to him is still pretty sad to watch. Watching him say goodbye to Carol was particularly heartbreaking.
• Before Kyle Rayner leaves Earth after being traumatized by the brutal hate crime inflicted on his gay assistant Terry, he tells his then-girlfriend Jade (Jennifer-Lynn Hayden, daughter of the first Green Lantern) about his insights into the human psyche during his time as Ion, and what they revealed to him about man's inhumanity to man, which unfortunately is still true today:
  Kyle Rayner: Jen, I can't do this anymore.
  Jen: Do what?
  Kyle Rayner: Protect Earth. I've been thinking about something Brainwave said a few months back. About what drove him insane. He said that he had reached into the minds of millions, and all he found was hate. When I was Ion I felt it, too. Jen, there is good in this world, but it doesn't measure up to the bad. In the hearts of humanity, there is anger, there is rape, there is brutality... there is hate. It took this happening to Terry to... ...to break me. I can't help these people now. I don't want to. Earth will have to get by without me.
  Green Lantern #155 (2002)
• Ch'p sobbing over how he's no longer married to M'nn'e because of how the Crisis altered the history of his homeworld after hearing of John Stewart and Katma Tui's engagement in Green Lantern Corps Vol 1 issue 211.
  Ch'p: WAAAAAAA!
  Katma Tui: Ch'p—?
  Ch'p: I lost my wife! I lost my wife an' my friends an'—an'— —my whole sector—! BAWWWWWWW!

---