In Episode 25 of season one after defeating the combined Hal/Al by the narrowest of margins, Colonel Sergei, who has been injured and his mobile suit crippled in the fight, orders Soma to forget about him and pursue Hal/Al. Instead she does the opposite, leaving Hal/Al and helping Sergei out of his ruined GN-X. When he asks her why she was disobeying, she simply replied that without him she'd be alone. Not much, but it beautifully showcased how much she had grown from the hard line, born-and-bred soldier she was when she was first introduced.
In Episode 7 of season two Soma Peries regains her memories/personality as Marie Parfacy and decides to stay with Allelujah. Then Sergei comes to escort her back, but she decides to stay with Allelujah, When Papa Bear is about to leave, Marie rushes towards him and hugged him saying: "The Soma Peries inside me has this to say: 'I wanted to be your daughter.'" This moment also doubles as a Tear Jerker to some fans
The Ending scene of Episode 16 when the other three Meisters helped an injured and tired Setsuna from Mister Bushido. After Bushido retreats, Setsuna collapsed and lost control of 00-Raizer. The other three Gundams carried 00 while Setsuna remembers Neil "Lockon Stratos" Dylandy as he is being carried back to their ship.
In Episode 17 of Season 2 A space elevator is coming down and chunks of it are starting to fall to the city below, the Gundams start shooting to try to blow them up but there's only three of them there and pieces of debris inevitably get through. Suddenly however the mobile suits from Katharon blow up the pieces that the Gundams couldn't get, then the Earth Federation forces start shooting too and we see a massive formation trying desperately to save the people below. Next mobile suits from the A-Laws arrive and for a split second everyone thinks they're going to start shooting at Katharon or the Gundams... until they take up positions in the formation and join in with blowing up the debris. All these people are at war with each other but for this scene we see what they could do if they stopped fighting and worked together. Then once the collapse is over a certain member of A-Laws goes and screws it up.
Episode 25 - The final episode of Season 2, while widely regarded as an episode full of Moments of Awesome, also has a heartwarming moment right when Setsuna faces off against Amuro Ribbons Almark one last time, with Marina's music played again and she herself commenting on Setsuna's determination as a soldier of tomorrows.
'Insane' YMMV will apply but Nena Trinity storing her wrath and working with people she despises, getting tortured physically, mentally and (implied in series, confirmed in an interview) sexually by Ali-Al, swallowing her pride, and a bunch of other things for survival. Not for herself, but for her brothers. Now, imagine you having to put up with 5 years of all of that, just so your brothers, who were killed before you, can be avenged. She did everything she could in that season, not for herself, but for her brothers, and considering how selfish she was for all of her life, it warms this troper up more than just a tiny bit to see the extents she's willing to go for a really, REALLY messed up family. In the end, one actually hopes that, in death, Nena will finally get to reunite with her brothers.
"Trust You", the fourth ending, is made of this.
This troper cooed like a baby when Tieria put a blanket over a sleeping Mileina and said, "I'm glad you're here with us, Mileina." Considering T-chan from the first season, this was just heartwarming and adorable.
Oh, and when the alarm sounds almost immediately after, the camera pans back out to reveal a sleeping Saji and Tieria holding another blanket, which means he was about to pull a blanket over Saji as well. Awwwwwwwwwwwwwww.
A fairly obvious one: After the war, Colonel- er, General Katie vows to keep an eye out for Celestial Being in case they start trouble again... But for now, she's getting married... to Patrick!
In the extended ending made for the special edition version, there is a scene where they are recovering all of the gundams and the pilots. Mileina presumably reporting that the Exia was not recovered like the others, with the camera panning to Feldt desperately searching for it, tears welling in her eyes, then Tieria points her to the flower she gave Setsuna, and with it Setsuna himself. The tears of relief were sweet, especially since it would have been heart-wrenching to have her Second Love die much like how her crush on Lockon ended up.