What a wide concept... no romance and no action... It can mean so many things... comedy, mistery, or something weird like Parappa...
Anyway, here are some titles...
Perfect blue - It's a movie, a psychological thriller (warning, some "almost naked" girls)
Monster - More in the line of death note, but with no paranormal things and a lot more violent (I don't think it can be considered as action... as 90% of the anime is dialogue)