The Good ending, where Tidus is given a real human life and appears on the shores of Besaid. The Celsius lands there; Yuna jumps out, runs over to Tidus, and they embrace.
Tidus: Whoa! You've changed!
Yuna: Well, you've missed a few things!
Tidus: I want to hear everything!
Yuna: Well, it all began when I saw this sphere of you...
Shuyin and Lenne's spirits finally reuniting.
The whole point of the game: Yuna trying to find Tidus, spurred by hopes that he is still alive somewhere.
You also gotta admit, unlike XIII-2 and the sequels to VII, X-2's Spira had a permanent change for the better. It is heartwarming to see that Spira is truly liberated from Sin, in no small part due to Yuna and company's hard work.
In the middle of the Gullwings charging for helping people out in Chapter 3, the Djose Temple is being attacked, and although they said they had it under control, it's getting worse and the others are all reluctant to help out. Rikku, knowing Gippal is probably there, snaps "I'll pay you myself!" and orders Brother to fly them there.
In Besaid in Chapter 5, Yuna receives a sphere from Chappu made on the day he left. Later on, Wakka names his and Lulu's baby Vidina, which is Al Bhed for 'future.' It shows Wakka is now more confident to be a father, and it's Fridge Brilliance when you realize that this shows just how far he has abandoned his old prejudice and hatred of the Al Bhed.
After Wakka names the baby, the Running Gag of him taking forever to come up with a name comes to an end.
Wakka: Hey. Sorry it took me so long to decide on a name, Lu.
Lulu: It’s all right. I knew it would be worth the wait. I had faith.
Wakka: You? Had faith in me?
Lulu: Wakka, we’re in this together. Whether you see it or not, I really do rely on you.
Wakka: Guess I’d better not drop the ball, ya?
Lulu: You won’t.
Paine's sphere where she, Gippal, Nooj, and Baralai talk about what they'll do once their time in the Crimson Squad is over. It's when you realize that Paine is indeed doing what she said she would for them.
The very last scene of the Normal ending, with YRP riding on the deck of the Celsius up into the sky.
When Yuna learns that the plan in the works to stop the Big Bad involves yet more people sacrificing their lives, she states with heartfelt emotions... that the plan SUCKS, and proceeds to wing it to a new one.
Yuna's performance of "1000 Words" at the Thunder Plains, despite the Tear Jerker nature of it showing the flashback of Lenne and Shuyin being gunned down. Best of all, after the concerts over Yuna learns that all the people who witnessed the event have come to realize how stupid they've been with their squabbling, and are ready to make peace with each other.
Personally, this troper thinks the English version is better. Instead of Lenne outright possessing Yuna to sing (like Shuyin would), Yuna sings the song with Lenne in a duet. It showed a subtle difference between Lenne and Shuyin. It also fits perfectly with the idea of a singer. Lenne didn't use Yuna, they harmonized.
While fighting Shuyin and Vegnagun in the Farplane, the souls of Auron, Jecht and Braska cheer on and offer advice to YRP. Even in death, these three are still guarding Yuna and Spira.
The Behemoth balloon salesman. His fellow Fiends are afraid of him so he can't sell his wares to them. However, the Kinderguardians appear, and don't care that it's a giant Fiend who's selling balloons, they really want to buy them. The other Fiends see this, realize the Behemoth salesman is genuinely trying to make a living, and they decide to buy some as well. The Behemoth was thrilled.