Lol at the people who are suggesting graphic anime just because of the violence...that doesn't mean shit
Shiki-Will cause severe emotional trauma along with a obscure yet realistic look on humanity
Psycho Pass- So many philosophies that are discussed in this anime can be and are directly related to human life, gives insight ( which I find correct insight) into becoming a superior human being and living a better life. Then there is the overarching idea that a "perfect world" can never exist.
Monster- Don't remember too many idea's that can help live life, however the plot and characters are way too complex to ever even hope of understanding without a rather mature mind.