First, Cloud floating near death and being healed by Aerith, with her and Zack joking about him being too big to adopt after Cloud calls her Mother. Even when they're dead, they're still looking out for Cloud. Cloud then wakes up in the Sector 5 Church with all of the people there.
The look on Cloud's face - embarrassed, amazed, happy as the kids crowded around to celebrate - and then when Aerith turns and walks away, and then Zack waves once and follows... and then Cloud looks at the kids again, and his friends, and Tifa, and the true moment is the line after the fade: "I'm not alone. Not anymore." Just...
Sephiroth: Tell me what you cherish most. Give me the pleasure of taking it away. Cloud: I pity you. You just don't get it at all. There's not a thing I don't cherish! Commence Omnislash ver. 5
In Advent Children Complete after Sephiroth has hit Cloud with an Octoslash and done some damage, Zack shows up to offer some encouragement and support.
Zack: So what if it looks hopeless? If it was me, I still wouldn't give up. Embrace your dreams, and no matter what happens, protect your honor as SOLDIER. Well, okay, you never made SOLDIER, but it's what's in here [Puts fist over heart] that counts. Cloud: Zack... Zack: So, need any help? Cloud: No. [Cloud starts to stand up] Zack: You already beat him once didn't you? This should be a cinch! Cloud: Yeah. Zack: Cloud, you know what I told you. Cloud: That's right, I am your living legacy. ''Commence Omnislash ver. 6
When Cloud drops his phone into a pool of water, we watch it slowly sinks, as we hear messages from all his friends. Then, when it finally reaches the bottom:
Aerith: I never blamed you. Not once. You came for me. That's all that matters.
Cloud saving Tifa from the falling building. Not really the moment itself but if you think back to the original game and Clouds promise. Yep she finally got her hero helping her out when she's in a bind.
In the special OVA that comes with the Complete version, Denzel tells Reeve the story of his life leading up to getting found by Cloud. One segment is about him being taken in by an old woman after his parents were killed in the Sector 7 crash. At the end, when Reeve is leaving, he tells Denzel, "Thank you for taking care of my mother."
Rufus leaping off a building to escape Kadaj with no means to save himself from the deadly fall. How can he do that so readily and coolly? According to Word of God, he's just that confident that the Turks will save him.
When Reno and Rude see Bahamut Sin, they freak out and run, but stop to pick up three kids that are under the white-haired trios' control (as they are so entranced that they don't notice the danger).
Kadaj mistaking Aerith for his mother, enabling him to pass on into the Lifestream. The dialogue between Aerith and Zack in the Lifestream is also heartwarming.