This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Lost Odyssey
Lost Odyssey had its moments in the main story - primarily the death of Kaim's daughter, moments after he's finally been reunited with her, after having believed her to be dead for 15 years - but it's in the sub-section The Dreams of a Thousand Years that the tears really start flowing. While having no impact on the actual game-flow or story, these tidbits of memory from Kaim's thousands years of life - watching people being born, grow up, and die, being happy or in despair, dying young or in ripe old age... with atmospheric music and artisticly-rendered background imagery, these simple, written tales don't just tug your heartstrings - they play them like a harp. Which is probably a good thing, since that's basically the only point of their existence.
Well, that and the achievement.
The ending, with all the characters inside or stuck outside the death-sphere thing, where you watch your friends, including the comic relief and probably most human of all the characters, die. Sure they get better, but still.
"Letters from a Weakling" deserves a mention: Kaim's friend Alex marries a woman named Myna and brings her to his home town, a small and insular village. Myna is of a different race and doesn't speak the language well; she tries, but no one in the village accepts her. The entire time, Myna writes to Kaim, lying about how happy she is - Alex intercepts the letters in order to read them and forges answers from Kaim telling Myna to stay strong and that he'll visit soon, while sending his own letters begging Kaim to visit. A while after having a child, Myna completely breaks down. She writes one last letter to Kaim which Alex does not send on, and after receiving Alex's forged reply - once again telling her to "stay strong" - she hangs herself. Alex visits Kaim to tell him about Myna's death. Kaim beats the crap out of Alex, who confesses everything, admitting that he wanted Kaim to support Myna because he was too weak to do so himself. The story ends on a happy note: Alex resolves to make sure his son is accepted as Myna was not, and when Kaim visits the village generations later, Alex and Myna's descendants live there side by side with the other villagers. Still, it's one of the sadder stories.
The very first story you unlock, 'Hanna's Departure', is about the daughter of innkeepers who befriends Kaim. Despite being extremely young, she has an unnamed condition that will kill her before she grows up. Unable to travel, she asks the patrons of the inn about their travels, having adventures vicariously through them and experiencing the world she'll never get to physically see. Kaim ends up finding a degree of solace in telling her stories, since he leaves out the details of his mercenary life of blood and warfare, instead choosing to focus on a flower he saw, or a ravine he drank from, or the sight of the ocean. The story itself is about Kaim's final journey to see her as she is unconscious and dying, and telling her about the adventures he's had since he last saw her. Even though she is dying in her sleep, Kaim tells the stories anyway, believing some part of her hears them. Finally, he tells her that she's about to start her own journey, and even as the immortal Kaim promises he'll see her again on that journey, he knows it's a lie. She Dies Smiling while he says they'll meet again.
Lirum's death, Seth's return through the mirror in the ending.