This next placement is a step up from the "Animation for Animation's sake" tier, since while they do have several scenes just for fun, the story of sorts is a bit more structured. Episodic shows are common here, but they'll be getting a place later.
http://www.ranker.com/list/best-entertainment-anime/heroicrebellion,
Ghost in the Shell: Stand Alone Complex
Gurren Lagann
Samurai Champloo
Baccano!
FullMetal Alchemist