Devilman, Saber Marionette J, Peace Maker, Hakuouki, Samurai Deeper Kyo, Blade, Blade of the Immortal, Samurai Champloo, Tenchi Muyo, Tokkou, Vampire Hunter D, Summer Wars, Golden Boy, Amon! Apocalypse of Devilman, Baoh, etc Also, I've noticed you've watched Discipline lmfao
Re Zero (an airing anime but its so good you should at least try its first episode)
Attack on Titan (this anime is the king of artistic style , action and horror ,amazing soundtrack , the story keeps getting better  and better each episode).
Clannad (Clannad After Story too) is one of the best anime you can find of its type ( A family one in season 2 , friendship in season 1).
Madoka Magica (try at least 2 or 3 episode before turning away from this .
gem, it has a good story of friendship and fantastic soundtrack, the art is also unique)
Nana (this is one of the best (the #1 in my opinion) grown up (mature) romance anime, it has friendship-romance-drama blended together beautifully , the story is being narrated by the MCs at the end of each episode , which is one of the best part of the anime.

I only recommended 5 (not 10) but that means you should at least try half (if not one) of these anime.
the longer the list the more difficult it would be to you to choose which one should come first .


Shonen etc:
Buzzer Beater
Blood+
Devilman Lady
Wolf's Rain
Captain Harlock
Koukou Butouden Crows

Shojo etc:
Yamato Nadeshiko Shichihenge
Skip Beat
Hana yori Dango
Nana
Vampire Night
Night Head Genesis


Dropped:
Kyou kara ore wa, Samurai Champloo, Afro Samurai, Trinity Blood, Rideback, Casshern Sins, Raxephon, Physco Diver, Great Teacher Onizuka, Gankutsuou, Ultraviolet, Xmen, Blade..