Judging by your personal taste and personal favorites I recommend these:
Puella Magi Madoka Magica(Fantasy, Psychological horror, tragedy, 12 episodes)
Neon Genesis Evangelion(Sci-fi, Psychological Horror, drama, 26 episodes and one movie)
Fate/Zero(fantasy, action, tragedy, 25 episodes)
Kara no Kyoukai(fantasy, action, drama, 7 movies)
Perfect Blue(horror, mystery, 1 movie)
Higurashi no Naku Koro Ni(horror, fantasy, drama, mystery, 50 episodes)
Now if you're talking about any genre:
Cowboy Bebop(Sci-fi, action, comedy, tragedy, 26 episodes)
Trigun(Sci-fi, action, comedy, drama, 26 episodes)
Fooly Cooly(Uhhh...comedy...I guess, 6 episodes)
Baccano!(fantasy, action, 16 episodes)
Summer Wars(sci-fi, drama, action, comedy, 1 movie)
Grave of the Fireflies(tragedy, 1 movie)
Tokyo Godfathers(drama, comedy, 1 movie)
Revolutionary Girl Utena(drama, arthouse, 39 episodes)
Mawaru Penguindrum(drama, comedy, arthouse, 26 episodes)
Bakemonogatari(fantasy, drama, comedy, 15 episodes)
Tengen Toppa Gurren Laggan(sci-fi, action, drama, 27 episodes)
I'm leaving many things out, but I think this pretty much covers it...sort of.