Lost Odyssey is a JRPG about an immortal amnesiac mercenary and his quest to regain his memories and discover his purpose. The game is mediocre at best, but the story is fairly good (and the music is excellent). This game made me cry (albeit I played it as a teenager, when I cried a lot more easily).
Particular points I want to praise the story for:
The main character is strong. He sees his immortality as a curse and his arc is about coming to terms with it. It's handled excellently, central to the plot, revealed in the beginning and resolved in the end; he has a very deep background that we learn about gradually throughout the game; and his emotional vulnerabilities complement his badassery. He isn't confined to a single mood; he behaves like a coherent, believable person. Most of the other characters are also really good, Seth in particular gets a shoutout.
The story makes very good use of child characters. Two of the party members are little kids, and they get both sides of things. On one hand, they save the adults multiple times, are playable in battle (they have magic energy), and have personalities that are more than stereotypes. On the other hand, they do act their age; they get scared of the monsters and hide behind the adults in at least one cutscene, cry several times, and do some really imprudent things when the adults aren't around and need to be saved by them.
The ending is excellent. While it's horrible that most of the explanation is hidden away in an optional dungeon, it all makes sense if you do understand it, there's no Deus Ex Machina and the triumph comes with a sacrifice and an awesome dilemma for the main character.
The game has good humor!
I'll also make a list of criticisms:
The battle system is a typical JRPG one. It's low-skill, and while normal fights are balanced so you should never lose, bad luck or being underleveled can easily trump good play in a boss fight. The amount of work you have to do outside of battle managing skill links and stuff is also a serious drag, especially since you can't see quantitative information.
Two of the party members are rulers. I don't consider it a deal-breaker because the story also keeps the evils of government offscreen and unmentioned, so it's more turning a blind eye than consciously justifying evil. It's only standard fare for a fantasy story.
There are a couple of scenes that invoke the misandrist trope of asymmetric violence rules, but it's not a huge deal because the victim is always a character who is one of the least deserving of glorification, and most of the time it isn't really legitimized; one of the times another character vaguely criticizes it, another time it's partially defensible. The worst instance is in a fairly hidden optional scene. So it's a massive improvement over FF13 in this regard.
The magic system is a typical obfuscated magic system, and it's used for a Deus Ex Machina at least once (when the Uhran mage teleports Tolten and Seth out of the snowstorm in Gohtza).
Both of the romances are poor. One pair seems to have no chemistry at all (it's actually very similar to Han/Leia except without the abuse) and the other is believable but it's a stretch.
Both villains are poor. One is a generic power-hungry world-conquerer (albeit he isn't strawman chaotic evil; his actions are at least plausibly explicable) and the other is completely incompetent and used for comic relief several times. On the bright side, he's legitimately good comic relief.
The nudity pandering is ridiculous. All four of the female party members are scantily dressed, and two of them have their breasts blatantly exposed. If you thought FF13 was bad...