The Light Side resolution to Ajunta Pall is exceedingly poignant. Here is one of the biggest, baddest original Sith Lords, whose ghost is wracked by guilt and torment, and you convince him his master will welcome him back if he chooses to return to the light.
Ajunta Pall: If… if I could return. Oh, my Master… it has been… so long… and I regret so much… (vanishes, having chosen the Light Side)
The scene in II where the Sith tomb hallucination makes you revisit Dxun, the bloodiest part of the Mandalorian Wars, is deeply touching. The path is mined, and you remember this as an unnecessarily, pointless feint where the soldiers died in vain. The commander asks you if they have to charge through, wanting their sacrifice to mean something.
Exile: Not this time. I'm going up there alone.
(You destroy all the mines yourself and lead them to victory, saving their lives)
It's even more heartwarming (although a bit funny) if you have no demolitions skill, meaning you have to set off the mines by walking through them.
Or you can use the destroy droids ability if you want to be safe while doing so.
Mira's cutscene, where she opens herself to the Force.
Likewise, the scene with Atton where he lets go of his anger towards the Jedi and decides to embrace the Force.
Exile: And at last Atton... awaken.
Kreia telling you"I would have killed the galaxy to save you." Coming from the orchestrator of the entire game and the final boss, that was unexpected.
The beginning of the action on Taris, when Carth reveals that he's not only gotten you to safety but has been watching over you for days. Not so obvious at first, but once you know more about him, you discover you've landed in the safe hands of a seriously Nice Guy
If you play light-side and female, the brig on the Leviathan, oddly enough. After he's singled out for "special attention" from his former commanding officer and mentor in the torture chamber as a means to break you down, Carth "I will never trust anyone ever again" Onasi says "I know you would never intentionally hurt me," and admits that, were your roles switched, he probably would've caved under interrogation to avoid making you suffer.
Mical telling The Exile, "…and where they look at you and see the death of the Force, I look at you and see hope for all life."
If the Exile is male, Visas will be the one who says the line.
Juhani's lines were Dummied Out for that scene, but talk to her afterward, and she is all choked up. Turns out you were the one who indirectly saved her life as a young girl, and later saved her life in the grove. She is humbled and awestruck by this. If you are Light Side, she is elated that you are once again the paragon she seeks to live up to. If you are Dark Sided, it turns into a borderline Tear Jerker as she resolves to help you back.
The good ending of the Feuding Families quest. If if their fathers are still at eachother's throats, Seth and Rashiana are still able to be together in the safety of the Jedi Enclave, and that's all that matters to them. Their heartfelt thanks to you is just the icing on the cake. A side order of Heartwarming In Hindsight comes up if you have Carth in your party. He gives his blessing, hoping that the young couple "knows the happiness I once did."
Game Mod example: In the Brotherhood of Shadow mod, Koybayashi's plea to "Sera Degana" to awake from her Angst Coma.
Also, Solomon's Heroic Sacrifice giving his life to heal Koybayashi, and finally making peace with his lost padawan, his Echani ethos, and the Force itself.
During the final confrontation on the Star Forge, a redeemed Revan asks for Malak's forgiveness and tells them they are sorry for setting him on the path to the Dark Side. Malak's response is that it was his fault for chosing to walk down it.
The end of Jolee's speech after The Reveal. Especially how sincere he sounds. "Does this change anything? I'm not here to judge you. You just do what you have to do. And I'll help if I can".