Don't make any plans because these shows might consume your life. Good animes tend to do that.

1. Attack on Titan

Recommended if you like:

Game of Thrones, The Walking Dead, very sad things constantly happening

2. Big O

Recommended if you like:

Batman: The Animated Series, Dark City, big robots

3. Death Note

Recommended if you like:

Hannibal, The Following, Orphan Black

4. Fullmetal Alchemist Brotherhood

Recommended if you like:

Inglorious Basterds, Indiana Jones, Harry Potter

5. Tengen Toppa Gurren Lagann

Recommended if you like:

Independence Day, Big Fish, The Wonder Years

6. Puella Magi Madoka Magica

Recommended if you like:

Buffy The Vampire Slayer, Teen Wolf, The Vampire Diaries

7. Neon Genesis Evangelion

Recommended if you like:

Pacific Rim, serious teenage angst, having your brain melted out of your ears

8. Rurouni Kenshin

Recommended if you like:

When Harry Met Sally, sprawling samurai stories, lots of action