Best new anime series (May 2016 edition)

Kabaneri of the Iron Fortress is available on Amazon Prime. Only 3 episodes so far but it's a great 19th century steampunk-zombie story.

Kabaneri of the Iron Fortress is also proof that steampunk is much, much more diverse than the stereotype of white people living in 19th century Victorian England.

Ajin: Demi-Human is available on Netflix and tells the story of people who discover they are immortal. A disturbing, fast-paced anime.

Boku Dake ga Inai Machi (Erased) is on Crunchyroll and focuses on a man who keeps falling through time to a devastating serial killer attack on his friends.

I highly recommend seeking out these anime series. They're innovative with strong characters and are extremely different from what you've seen before.