The entirety of On a Silver Night, the Heart Does Not Sway on the Water's Surface.... Every bit of it, but especially the deaths of Bertha and Itzhak.
Episode six. Poor Havok...
And, assuming you can figure out what the hell is going on, the last episode. Amber was doing the whole thing to try to make Hei happy, and he never wanted to kill anyone in the first place. Perhaps also the bit after Amber turns back time a couple of minutes to give Hei another chance, when we see the Syndicate completely ignoring the fact that there obviously isn't a threat in favor of trying to wipe out every contractor on the planet.
The end of episode four. "I'm back." "Welcome home, dads."
Kirihara in Shikkoku no Hana reaching a crime scene, saw Hei and Yin entering a portal. Her reaction? Running there extending a hand in open "wait for me!" gesture and screaming "Stop! Li-Kun! Li... <portal vanishes>". So she just stops there with a hand still thrust forward and makes such an adorable sad face that when she gets distracted by seeing a corpse "flung all around" it couldn't be as bad.
The entire OVA, Hei and Yin's life begins to crumble around them with Hei going through serious physical trauma and being slowly worn down by the multiple Contractors who have been sent to kill him. While at the end Yin demands Hei kill her in order to stop her super powered evil side being released. Hei refuses, promptly loses Yin, and is driven to drinking in the most tragic story arc of the franchise.
The death of November 11. After finding out that death was inevitable courtesy of the future-seeingAmber, November 11 confronted his boss and killed him and a bunch of bodyguards, completing his mission...with nothing but a bottle of brandy. The last phone call brings out the tears, but seeing the dead bodies of Decade and his henchmen also solidifies this Tear Jerker as a Dying Moment of Awesome.
The tidbits of the last episode in Gemini of the Meteor when Misaki narrates.
Hei holding Suou closely, trying to comfort her, as her memories fade away.
The fourth to last episode: everything is building up for the finale, and Kirihara and Li/Hei are hanging out eating, playing baseball and laughing. Kirihara laughs at Li, and you realize that no matter what he did, Hei could never make his sister laugh like that.
Huang's backstory. He met and fell in love with a girl, who unknown to him, was a contractor trying to find out whether he or his (working) partner was a threat to the Syndicate. It's implied that he hadn't been with many, if any, women due to his looks, and that he may have been jealous of his partner having such a lovely wife. One day, after walking back from dinner with his partner, the partner is killed by Huang's girlfriend with her brutal contractor powers, before she leaves, never giving him an explanation. When Huang meets her years later, although he realises he shouldn't still care about her, his concern for her leads to him botching the mission. He's ordered to kill her after she's helped with the follow-up mission, but she reveals that her remuneration is that she feels remorse for what she does, leading to him hesitating. Eventually, after some agonising he decides to run away from the Syndicate with her, as she has revealed that she really did fall in love with him all these years ago. Hei even agrees to let them go...and then she goes and throws herself in front of a truck, since another Syndicate agent had spotted them and would have killed the two of them if she hadn't done so. Makes you want to give the poor guy a hug.