A mix of this and Tear Jerker, but Zidane telling Dagger about the man who tried to find his true home and came to realize that his true home was with his adopted father. (Aka, Zidane's first time he left Tantalus.)
Zidane: Once upon a time... ...there was a man. There was a man who didn't know where he came from...
Zidane: This man had longed to find his birthplace ever since he was a small child. His birthplace. A place he only remembered in his dreams...
Zidane: He wanted to know more about himself, maybe. About his place, the house where he was born... One day, the man left the home of his adoptive father and went on a quest to find the answer. His only clue was the blue light he saw in his dreams..."
Dagger: A blue light?
Zidane: Yeah. He thought it might be a memory of his birthplace. An ocean, maybe...?
Dagger: Did he find it?
Zidane: Hey, you're jumping ahead. A lot of things happened along the way. Alright, we can skip ahead... No, he never found it. How could he? His only clue was a colored light. So he went back to the home of his adoptive father... What do you think his father did when he came home?
Dagger: Welcomed him home?
Zidane: No way! The father raised his fist and beat the son he had worked so hard to raise.
Zidane: "I don't know... But you know what surprised him even more? The father smiled, after beating up his son! Can you believe that? He just gave his son a beating. But this is what the man thought when he saw his father smile... This is my home. This is the place I call home. The man is still searching for his birthplace. But he already has a home.
Zidane and Vivi's friendship. From the get go, Zidane is the Big Brother Mentor who pretty much always has Vivi's back and damned if anyone's going to change that.
Funny as it is, the love letter mishap which ends up being from Steiner to Beatrix is a very heartwarming and beautifully romantic event.
The cutscene where Dagger is on the crumbling tower and Zidane (in a BDH moment) comes out of nowhere to rescue her. You catch your breath as she looks at him in total disbelief of the fact that he is actually there, before she desperately grabs on to him for dear life. Then, as the tower falls away, she gives him this look and a hug of such loving gratitude that it melts your heart into a puddle of mush.
Especially when, for a moment, it looks like they're going to die. That Zidane willingly jumped to his death (so it seemed) to be with Dagger when she needed him is one of the most touching moments of all time.
The final scenes of Final Fantasy IX Zidane, thought to have died at the Iifa Tree, turns out to be alive and kicking. While Queen Garnet watches the "I Want to Be Your Canary" play, Zidane (disguised as the male lead Marcus) throws off his cloak and yells, "Bring my beloved Dagger to me!" A shocked Garnet then runs down the stairs, shoves her way through the crowd, and although her pendant falls off, she jumps towards Zidane and they embrace onstage while the crowd cheers and applauds. This editor was crying waterfalls. The whole thing's made even more heartwarming by the song that plays as the credits roll, "Melodies Of Life."
While undeniably a major Tear Jerker, the fact that Vivi is living in heaven after death is nothing short of a (somewhat) suitable reward for this young Black Mage, especially after all he's been through!
"Farewell. My memories will be part of the sky."
This troper particularly liked how at first, Garnet thinks that Steiner and Beatrix are going to stop her (Steiner having been no fan of Zidane throughout the game), but in fact they both open the doors for her and smile, basically saying without words "Go to him. It's okay."
Also, her throwing her crown to the ground just before she leaps into his arms. Really hammering home her feelings of "screw everything else... you're alive."
And this troper liked how the first reaction of Garnet is pound on Zidane's chest in a "why did you leave me alone" rage which she cannot sustain for more than two seconds before she totally melts. Really, do we think cutscenes really need voice acting?
How did you survive...?
I didn't have a choice. I had to live. I wanted to come home to you. So... I sang your song. Our song.
The scene preceding the ending is nearly as heartwarming. Despite everything Kuja had done, despite all of the misery and bloodshed that he was directly responsible for, and especially despite what he had personally done to Dagger and Zidane's friends, Zidane heads back into certain death to be next to Kuja on his deathbed. Because, when it comes down to it, that's what family does for each other.
The bit immediately after that one is also fairly heartwarming, in a weird way. After Zidane and Kuja's scene ends, we cut back to the outside, where Mikoto, is delivering a bit of a eulogy for Kuja. Because in the end, despite all the horrible things he did, he brought the Genomes hope that they can have a purpose in life beyond being the shells they were designed to be.
Let's explain the You Are Not Alone scene in detail. Zidane is told by the Big Bad that he was an 'Angel of Death' created to destroy all life of Gaia so it could be taken over by Terra, and he would have been the one who had essentially ruined his friend's lives with death and destruction. Then, after getting his soul partially drained, he crashes hard into a Heroic BSOD, but not only do his friends not judge him for what he is, they fight alongside him as he tries to push them away; he was there for them during the worst moments of their lives, so they're going to be there for his.
This troper's particularly fond of Steiner's in the sequence. Steiner has been adversarial at best toward Zidane for the vast majority of the game. But when he's freaked out, Steiner says in no uncertain terms that he will not abandon Zidane.
Steiner: I shall follow you to kingdom come if I must.
A huge part of Steiner's character development is him coming to terms with a lot of things, including his relationship with Zidane. Which makes that statement all the more powerful, and Steiner such an awesome character, to this troper as well.
"Beatrix... I will protect you!"
The story Zidane tells Dagger in the Inn of the Black Mage Village about "a place to call home".
What felt so heartwarming to this troper was during the beginning portion of Disc 4 when the Genomes start living with the Black Mages. Given how similar the two species are, having them interact with one another as they discover the wonders of life with their shared camaraderie is touching enough, but it's Zidane's moments with Mikoto that was absolutely adorable - he tells the black mages to care for her and he tells Mikoto to make lots of friends because "big brother" said so. That was a pile of heartwarming and cute right then and there.
The birth of Bobby Corwen the chocobo. Every other black mage sans the leader left with Kuja out of desperation because he promised them he would extend their limited life span ( he was lying) except the two black mages who stayed just so they could take care of the egg. They risked what could have saved them by being selfless and caring for something that means so much to the both of them. When the chocobo finally hatches, the two black mages cheer and get teary. 'Cuse me, I think I got something in my eye, too.
Eiko, at the very end, is adopted by Regent Cid and Hilda. She calls them "mother" and "father", much to Cid's surprise and delight.
During the events of Burmecia, Vivi worries out loud that he might not be human. Cue Quina coming along with a surprisingly touching response.
Quina: I not human. But you, you definitely human.
In the same vein as above, Steiner's interactions with Vivi. Steiner can be extremelyobnoxious at the beginning of the game, so thankfully he gets a truckload of Character Development. The one thing that never changes, though, is how much respect he has for Vivi. The culmination of this is probably when they go to the wind temple together:
Steiner: (re: a giant wind dragon) You attack him with your magic while I hold him down!
Vivi: But...what if I miss the target?
Steiner: I trust you, Vivi.
*and then the two of them proceed to beat up Tiamat all by themselves*
When Vivi is held captive in Dali, you can go back to the pipe where you first heard him crying, only to hear him crying again. Zidane's quiet for a moment, before whispering 'we'll get you out'.
In Disc 2, when Zidane tells Dagger that everyone who helped her was following his/her own path, Dagger asks Zidane why he came with her. In a surprisingly romantic and sweet moment, Zidane uses a quote from a play as his answer: "Only because I wanted to go with you." Awwww!