On top of my mind:

Death Parade: Go. Watch. It. Right. Now.

Erased: One of the best anime I watched in a while. It's about a person with the ability to go back in time to re-live certain events of his own life and the possibility to change the outcome.

Devilman Crybaby (Netflix): This is just a masterpiece, even though it's not for everyone. The animation style is very unique, there is A LOT of blood, gore and violence. Story and characters are amazing.

A couple of more recent shows:

A.I.C.O Incarnation (Netflix): I finished it today and I thought it was pretty good. It's a sci-fi anime with good action, story and main characters. It's only 12 episodes though.

Saga of Tanya the Evil: I was skeptical about this one at first, but it turned out to be really fun and entertaining to watch thanks to great action, comedy and a really good main character. The first episode may seem weird, but the second one explains a lot of what happens, so wait at least until get to that.

What about some classics like Evangelion? Also, since some people already suggested Nana, I'm going with Ancient Magus Bride. Jojo is a must watch.