I only played four new games in 2016, so:
Fire Emblem FatesIt took things that I liked about Awakening and made them better. I like the new team-up mechanics, I like the way weapon degradation is handled (or not handled, as the case may be), and I like the way that powerful weapons are risky to use. It also took things I disliked about Awakening and made them worse. Wow the story in this game is garbage. At least the voice acting is decent.
Rhythm Heaven MegamixI've already talked about
my thoughts on Rhythm Heaven, so it shouldn't be any surprise at all that I loved the hell out of this game. It's exactly what I wanted: more distilled happiness and tricky rhythm challenges. The series so far has done just fine with no narrative, but I enjoyed the dialogue bits a whole lot. I don't think it took away from the game.
OverwatchI haven't had this much fun online since Team Fortress 2.
For real though, it's good to have a game that I play with friends, to keep us connected and having a good time. Plus, the game is really quite fun. Learning new characters is a fun process, and there's nothing quite like the feeling when your team coordinates well and succeeds in a big push. Definitely one of my favorites.
Final Fantasy XVI like it, but also it's got some real problems. Story pacing is kinda weird, conveyance can be problematic, and also there's a lot of bugs. I'm also waist-deep in sidequests and haven't progressed very far in the story, so it's tough to judge. I'm having a good time, though.
Honorable mention also goes to
Bloodborne, which came out in 2015, but I started playing in the summer of 2016. I liked Dark Souls, but not enough to have me chomping at the bit for more. Bloodborne changed my mind; it's faster and more stylish than Dark Souls, and tells you more of the story while still maintaining the air of mystery that the games are known for. I love it and will probably play through it more than a few times.