You can find all of these on kissanime.com
Series
Neon Genesis: Evangelion (action)
FLCL (action)
Shingeki no Bahamut (fantasy / action)
Hoozuki no Reitetsu (gag comedy set in hell...fantasy?)
Movies
Akira (action)
Ghost in the Shell (action)
Patlabor: The Movie (action)
Patlabor 2: The Movie (action)
Other good stuff
Tatami Galaxy
Dennou Coil
Nasu: Summer in Andulasia (movie)
Kaiba
Ping Pong the Animation
@(you need an account to see links)
If you want to be entertained for a few years, watch One Piece
No, seriously, it's the best anime you'll ever watch
wvereeck (08-12-2015)
Zeus (08-11-2015)
I highly reccommend Code Geass and Death Note :*
Those two got me deeper into the anime world.
my fav ones are inuyasha, kuroshitsuji, yu yu hakusho, hellsing and i cant really remember everything!!
Death note,Fullmetal alchemist,Naruto,Bleach
I second Full Alchemist, Deathnote, Deadman Wonderland, Elfen Lied, and Blood+.
Also watch Mushi Shi, Attack on Titan, Shiki, Highschool of the Dead, and Tokyo Ghoul.
AND READ ALL THE JUNJI ITO MANGA IF YOU REALLY LOVE HORROR
I don't watch a lot of anime at all. But I have recently watched One Punch Man. It has some pretty awesome action in that anime. Also another one I would recommend is Hunter x Hunter. It actually has A LOT of episodes, and it is partially on Netflix. But I was literally glued to that anime most of the time.