Persona 3: FES (minus The Answer section)
A dark, emotional and engaging game. Grindy (but addictive) RPG battles that take place at night are broken up by a school-life/dating sim in the daytime. Added to both of these types of gameplay is Persona husbandry - you collect Personas as you go (a kind of spirit that is attached to you and gives you your fighting powers), and you can fuse them in different combinations to bring out different abilities.
The Personas are based on mythological beings from cultures around the world and the game handily includes an encyclopedia that lists a little bit about the history of each one, which is interesting to read if you feel like a bit of downtime from any of the other elements of the game.
Persona 3's story is well written throughout. Events change the world and your characters fundamentally as you progress. You also meet new people to add to your team along the way. Funny side stories like school trips lift the mood and make sure the overarching must-save-the-world-from-ending stuff doesn't get too emo.
I haven't played The Answer section of the FES edition so the jury's still out on that one, but just the main P3 game is fantastic on its own and wraps up in a truly epic ending. I recommend buying FES even if you only plan to play the main game and not The Answer, as the game is an updated version of vanilla P3 with some nice additions.
One warning: you'll need some time to play this. I'm a must-do-everything type with RPGs and this took me 120 hours to get through. However, I've heard it can be finished in 70-80 hours if you play it in a more streamlined way. Personally I consider the length a plus as I like my games to seem almost unattainably long (makes completing them that much sweeter), but nowadays a lot of people seem to prefer 10-20 hour jaunts, which this definitely ain't.