Yuki-Rin rescuing Kazuma and giving him a new home after his old home burned down.
Kazuma's promise to his dad. After he makes his promise, his dad comes out of his coma.
Baleeria Porto Arc
During Drusilla's flashback, the scene where Rob Lucci accepts her into Cipher Pol for her fighting abilities. It's made even more heartwarming when you realize that this incident is probably the first time anybody had accepted Drusilla after her father blinded her and committed suicide.
After Big Margo almost kills Molly, Yuki-Rin - Molly's adoptive sister - is devastated. She tries to be a Stepford Smiler in the faces of her nakama, but she breaks down when Kazuma comforts her and re-assures her that Molly will be okay.
After getting expelled from a Tenryuubito-run boarding school, Holden expects that his parents or a servant will pick him up, which means that slavery or death is a possibility. His parents or a servant don't pick him up. Instead, Soren, his older brother does. As soon as they leave the school, they decide to make a pact to find Heathcliffe and stay with him no matter where he is.
When Heathcliffe is reunited with Holden and Soren, his two brothers, who then join the crew.
Ginling Island Arc
Toward the end of chapter 14, Yuki-Rin is kidnapped by Roscoe Delacroix, who is a boy who chosen to be in an Arranged Marriage with Yuki-Rin before she became a pirate. Kazuma steps foward to lead the rescue party and save Yuki-Rin. Why? Because he is in love with Yuki-Rin. Awww...
Chapter 15's title is "I Love You, Yuki-Rin". Now, consider the fact that Kazuma is one of the viewpoint characters of the arc and that all of the UST between him and Yuki-Rin is about to be resolved after Kazuma defeats Roscoe.
In chapter 16, Kazuma is comforting Yuki-Rin when she is in the hospital after the battle against Roscoe, when this happens:
Kazuma: "Are you still scared?"
Yuki-Rin: "Yes." (Kazuma smiles)
Kazuma: "I know something that will make all of the hurt go away."
Yuki-Rin: "What... What is it? ( Kazuma then kisses Yuki-Rin) Kazuma... I forgot to tell you this earlier. I... I love you."
Kazuma: "I love you too, Yuki-Rin. I want to be your Pirate King."
Ghost Ship Arc
In chapter 20, Aki is resting in Heathcliffe's bedroom after being attacked by Kaoru back on the Ghost Ship, and Heathcliffe was made to watch her in case her condition got worse. They are talking to each other, and, they then realize that they will make good friends.