Ori and The Blind Forest was soooooooooooo good
, I finished it all in one day, hehehe.
Nowadays there aren't many games like that, but one that I can really recommend is Rayman Legends, it's just awesome. Rayman is more comedy and great plataformer, but is really good, for me one of the best games I played in recent years (and best part, can also be played Co-Op).
As for the emotional part, I really recommend Valiant Hearts (the ending of this game is one of the most emotional I have ever seen) and Child of Light (this one is kinda of a RPG). I also would recommend Bastion and Transistor, those are indie games, but they are really good.
From the games I recommended Rayman is the closest one to the style of Ori, but I really do recommend the others for the aspect of Fun/Emotional style of games. Hope you like them because I really did :p.