I could suggest: Metropolis, The Place Promised in Our Early Days, Voices of a Distant Star, Grave of the Fireflies (Caution: Extremely Sad), Jin-Roh: The Wolf Brigade, as well as Perfect Blue. Hope that helps.
*bows* Hello, everyone. To quote from a certain fanservice-heavy anime from a little while back... "I know I am not perfect, but I hope you will accept me." Thank you. :3