When Serge finally returns home after forcibly switching bodies with Lynx, most of the people in his village regard him with contempt. But when he goes to his mother...she doesn't freak out, she doesn't call him names. Instead, she simply asks to hear what's been going on, and never doubts for a moment that the creepy-looking panther man standing in front of her is her son.
Serge comforting and hugging Marcy in Hermit's Hideaway after Viper's near death.
The Golden Ending. After you use the Chrono Cross, everything becomes quiet for a few seconds, then Life ~ A Distant Promise starts up, Schala breaks free, and Lavos begins to dissolve. After playing Chrono Trigger and seeing Schala suffer so much, it's wonderful to see her finally get a happy ending.
When you go and get Pip to rejoin the party after "that event" happens.
Pip: It's you? Serge? It's okay. It's the inside that counts.
Solt and Peppor's reconciliation with Karsh at the Isle of the Damned:
Peppor: Looking back now, you were the one who took us under your wing, even though we were dragoon outcasts. You are very special to us, Sir Karsh!
Van's parting with his father when he joins your party (particularly how he starts rattling off common-sense things for Gogh to do while he's gone, like making sure to eat properly, dress warmly, not let the paintings get wet or ruined) and how his father gives him a boomerang "because they always return to you". Also the part with him in his room, listening to the seashell and remembering his mother, which has a Call-Back when you take the shell to his rich father in the other world.
When Draggy sees the skeleton of his mother. He starts crying because he's all alone, then his mother's spirit comes tells him that he's not alone, because he has friends with him. Then, he stops crying and says that "as long as he has friends, he will never be alone."
Also, his introduction. He has just hatched, and is looking frantically for his mother. Then, he turns to Lynx and asks "Will you take me as my mother and father?". Awwwwwwwwwwwww!!!!
A few mini-events where a character is reunited with someone close to them:
Finding all of Skelly's body parts and meeting his grandma again.
Take Karsh to Zappa and Zippa in Home World. Remember that Home World Karsh, along with the rest of Viper's group died at the Dead Sea 3 years ago, but his parents don't have any idea what really happened to him. Karsh realizes that it doesn't matter if he is the alternate world version of himself — he is still their son.
The end of the Dario sidequest. If you enter Home World's Viper Manor afterwards, you see that there are people hard at work remodeling the manor into an orphanage.
The "General Kid" alternate ending is basically what would have happened to Serge if the plot hadn't happened: engaged to Leena (who is significantly more affectionate than her opening scene) and apprenticed to a fisherman who says he's a natural. The sharp contrast of this "domestic tranquility" with the time-space adventure underscore the happy vibes.