I see. Well, I did mention "Mawaru Penguindrum" already. Believe me when I say that anime, despite its childish appearance, is a hard psychological story worth watching. Another one I would recommend, if you are looking for something that is simply a little life drama with some fantastical elements, I would recommend "Nagi no Asukara". Then again, if you are still looking for something with psychology, I would recommend "Psycho-Pass", but if you wish for a movie that might just make you cry, I say to give "Ookami Kodomo no Ame to Yuki" a try. The last one I would say is a must for everyone, unless you are a hard-core fantasy-lover and dislike seeing something that is, for the most part, slice-of-life. And there is my personal favorite "Wolf's Rain", but you should be ready for some context reading there. XD

Are there any notable animes you would like to mention? I still have more on my list, many actually, that I would say are worth watching.