In the Anime, Ume tearfully asks Ikki if he knows what he's getting into because if he goes through with joining Genesis, he'll be their enemy, and she doesn't want that as she considers him part of their family.
After Ikki challenges Yoshitsune, he is made to jump the Devil's 33, a 33.3 meter jump with barely any room to build one's momentum beforehand. While this would normally be difficult enough, the challenge also has the rider's team lying down shoulder to shoulder from the start to the finish, making any mistakes the rider makes quite costly for any friends who happen to be under him. Without being asked, Ringo lies down at the very end (considered the most dangerous position, and for good reason), and she isn't afraid because she knows Ikki can do it. Then, he screws up and is about to land on her, and twists aside, fucking up his knee in the process. This scene is the one that really defines their relationship: Ringo has absolute trust and faith in Ikki, and he would never think of letting her get hurt.
Ikki and Ringo's first kiss.
Kururu consoling Ikki immediately after he has a Heroic BSOD regarding Sora's true nature.
During Lind's first appearance, he dismisses Yayoi as "one woman out of four billion and easily replaced," and Agito goes berserk. It's always nice to see that Agito can care for someone else like that.
And after Agito retakes control, Lind smiles softly, looking rather happy that Agito and Akito had found a place where they belonged and that they wanted to fight for. Given the later reveal of Lind's true identity as Gazelle, that moment makes Lind seem like a mother who is proud of her children.
Ringo's confession to Ikki:
"Croissant Mask has a final message for you from Ringo. Ringo... loves you, Ikki. I love you."
Ikki's (second) Love Epiphany, where he finally realizes his feelings for Ringo. You really see how important she was to him, even when he thought their relationship was brother-sister, when he starts viciously kicking himself for inadvertently hurting her for so many years.
Mikan stating that she sees Rika as her own mother, and that she would do anything to make her happy. And then Ikki tells her that he will go save her because nobody else can.
Near the climax of Ikki's fight with Utgarda-Loki of Sleipnir, Utgarda (who is Desperately Looking for a Purpose in Life) tells Ikki to take him to a place far from where they are now, Ikki's monologued response is this: "Somewhere far from here...? Not my problem, dick. In fact, I need to get back. I've lost a lotta things that are so important to me... and I need to go and get her back." This is said as the scene changes to Ringo waiting alone at the edge of the Trophaeum Tower. As this was said in the wake of her confession, it's like Ikki regrets not answering her in kind, and getting back to her so that he can do so is now one of his primary motivations for fighting.
Arthur and Shalott's relationship. First off, Shalott gets most of his organs kicked out of his body byNike because he was trying to protect Arthur, who was falling behind in Nike's training. Then, Arthur willingly gives Shalott his own organs so that she can live, leaving him attached to her by and dependent on what amounts to an umbilical cord, and he tells her that he's happy that he's finally found a place where he belongs. Shalott kicks him, then softly tells him that the blood coming from his body is "warm and feels nice." One part squick, two parts heartwarming.
A small moment in that flashback: when Nike is just about to start killing Arthur and Shalott, the ship's captain comes and tells him to report in to Sora. As Nike walks away, the captain winks at Shalott, and Shalott gives him a thumbs up, thanking him for saving their lives.
Ikki gently thanking Kurumu for her efforts to keep the ship together. Even when he tuned with Ringo instead of Kururu, it was sweet to see him not forgetting her.
Ikki's (roundabout) confession to Ringo. For context, Kururu is preoccupied with keeping everybody alive and so cannot tune Ikki. Hako comes in and volunteers and Ringo shoots her down, because, in her own words, she's "Kururu's number one supporter." She truly thinks that Kururu will be able to do more for Ikki than anyone else, both on a practical and emotional level. Then Ikki speaks up with a simple, "Ringo, you do it. You're the one who's always been closest to me, right?" After years of not being able to get her feelings across in an emotionally satisfactory manner, he understands anyway and reciprocates. Victorious Childhood Friendindeed.
In the last chapter, Emily finally confesses to Kazu. He obviously accepts, causing her to start crying.
Ikki stopped wearing his first pair of A-Ts after they were damaged in his fight against Ringo and he refused to get them repaired as he wanted to create his own set of wings for himself. However, he refused to throw them away because they were a gift from Ringo, and in Chapter 353, it's revealed that he's wearing that exact same pair of A-Ts. It's clear what he's saying: Ringo gave him his wings, and that's the way it should be.
It's also pretty heartwarming how Ikki entrusted the Storm Regalia to Ringo. Sure, it was for the purpose of bending the rules to give them a critical advantage over Sora when they really needed it, but the fact that he trusted her with it says a lot about how much faith he has in her.
Rika telling her mother how Ikki, Ringo, Mikan, and Ume are her family and more important to her than the world.
The fact that this is the cover of the very last chapter of Air Gear is pretty heartwarming in and of itself.