It turns out there are some anime best described as abstract, that is stories that don't adhere to traditional narration, character development, or style and choose instead to convey their message through a more singular approach, but which are really worth your time? This list ranks the best anime representative of the abstract, including older titles, as well as new abstract anime that you may not know about.
One example is Mononoke; the title refers to spirits that pull from negative human emotions. The protagonist, known as the "Medicine Seller," takes on the mononoke during his travels and with his intellect, is able to defeat them by figuring them out. This anime falls under the "occult detective" genre. Another good abstract anime is Kaiba, a sci-fi story produced by Madhouse that deals with the heavy topic of memory theft. The main character is Kaiba, who begins the story with no memory, only to find that he is actually the king of memories, Warp.
Don't see your favorite abstract anime already? Add it to the list, so others can vote on it too!
Gankutsuou: The Count of Monte Cristo
Yojouhan Shinwa Taikei
Hikaru Utada: Passion
Eden of the East: Falling Down
The Diary of Tortov Roddle
The Diary of Tortov Roddle Specials
Hikaru Utada: Fluximation
Catman Series II
Catman Series III
Strange Story of a Dream Sphere Dealer
L'Œil du Cyclone
Kanashimi no Belladonna
Spring and Chaos