Three that I can think of off the top of my head include Ergo Proxy which is a futuristic world almost barren of life, and man is mankind is confined to mechanized domed cities where A.I.’s control all aspects of life. People aren't born but made and live side by side with the android servants. This construced paradise that houses its wealthy citizens and unfortunate immigrants is ruled by a mayor and his governing council. They demand that complete order and servitude is kept within Romdeau to keep chaos at its gates at bay. However, this utopian landscape is soon shattered by a series of horrifying murders. Re-L Mayer, a female inspector from the Citizen Information Bureau, along with her AutoReiv partner Iggy, are tasked to solve the murder cases.When Re-L and Iggy investigate the latest crime scene, Re-L is almost attacked by a mysterious creature, neither human nor AutoReiv, that is seemingly drawn to her. She begins to learn the truth about the mysterious creatures that are simply referred to as "Proxies" and what they truly are. - I just copied a short summary because when I try to explain it there seems to be a never ending stream of words..
Paprika- which I haven watched yet but seems to be promising is about a device that is invented to where people can record and watch their own dreams. Of course then a thief comes in and starts messing with people using the device and its up to Paprika to figure out who it is while also protecting her own mind.
Death Note is one that I haven't watched yet but have been told great things about. A boy named Light finds a book that has Death Note on it. It says that any name wrote inside will result in that person dying. There is a movie and a series to this, but I would recommend the series instead.
