Someone suggested Baten Kaitos: Origins, but that's actually a prequel to Baten Kaitos: Eternal Wings and the Lost Ocean. So if you can, definitely pick up that one first.
Someone else suggested Enchanted Arms, but you might want to watch some gameplay videos. I found the gameplay impossibly boring. Actually, you should probably watch short gameplay videos of anything before you go out and get it.
A lot of people are saying not to go for it, FFXIII was one of my favorite games, and I had a lot of fun playing it. I'll admit, it's really hit or miss: the battle system focuses more on strategy than skill, it's very linear, and it gets kind of tiring in the sense that all you do is go forward, fight monsters, go forward, fight monsters, without any real breaks throughout the game (though this serves to further emphasize the few parts where you DO take a break, as well as further convey the tone and theme of the game).
Anyway, there's also Parasite Eve and its sequel for the PS1. Short, but sweet. Radiata Stories for the Ps2 is pretty obscure, but there's an Unskippable episode on it, so check that one out as well. Atelier Iris 2 for the ps2 was a lot of fun (you don't need to play the first one to know what's going on, and the first one wasn't really as much fun in my opinion, and I haven't gotten around to three yet to have an opinion). As for some more current gen stuff, I'm currently playing a wii game called Fragile Dreams: Farewell Ruins of the Moon, which is freaking amazing so far. And if you like old school games, Nostalgia on the DS is certainly deserving of its title.
And, like everyone else has said on here, ATLUS GAMES AND CHRONO TRIGGER.