>>258102Child of Light is turn-based and has a pretty good story and soundtrack imo.
Odin Sphere, PS2 game. Just got an upgrade to the PS4. Beautiful game. Not turn-based but again, the story is pretty good.
Life is Strange (Telltale style play through the movie kind of thing. Choose wisely.)
Remember Me (gameplay is meh because I don't like playing with combos but the story was pretty good)
Heavy Rain, Haven't played it myself, but I've heard good things about the story. Multiple endings if you're into that sort of thing.
Kingdom Hearts series (have you been living under a rock?)
Final Fantasy, though I assume if you know you like turn-based and jrpg this is a no brainer...
Eternal Sonata is Jrpg and turn-based from what I remember...
Agree with other anon about the Persona games. I personally liked 3 the best so far, but that's just me. MAKE SURE YOU GET FES IF YOU GET 3!!! Currently waiting to play 5.
Sorry for the shortish list but that should get you going at least.