Great story, great characters, challenging turn-based system...this game sets the new standard for JRPGs
That said, in summary this is the best Xbox 360 JRPG right now and possibly the best JRPG ever made in a long time. The story is well crafted and the characters are all fleshed-out very well, and each of them are given their own moments to shine. The turn-based combat brings the concept to a whole new level, requiring you to cast buffs (defensive magic) to survive even regular enemies, and the boss fights are a whole new world of challenge entirely. You can't just choose 'Attack' all the time and expect to win. You have to play strategically and that is what makes the turn-based combat execution in this game extremely satisfying.
The dream sequences are well-crafted and do add to the story by making you appreciate who Kaim is and what he's been through. Sometimes events in the dream are even referenced in the actual game, so they're not simply 'attached' to the game, they're really part of the story.
Lastly, the Nobuo Uematsu's music is just immaculate.
Lost Odyssey is a true masterpiece, the true successor to the Final Fantasy series.