Creator: written by Dai Satō and directed by Shukō Murase
Basic Premise: In the future, people live in a domed city named Romdeau that protects them from the after effects of a world-wide ecological disaster that took place several centuries earlier. Humans living in the city are served by androids and robots. The outbreak of the cogito virus inflicts self-awareness on the automatons who catch it and causes the infected machines to start murdering humans. Behind the scenes, the government of Romdeau secretly performs experiments on a life form known as a "Proxy," which may hold the key to human survival in a nearly dead world.
Plus the opening song "Kiri" by Monoral is the best intro music for any anime, ever.
Other Notes: This is another one that gets deeply philosophical. For example the "cogito" virus and the title "ergo proxy" call to mind Descartes. The series makes frequent inquiries into the nature of the self and one's raison d'être. Additionally a rather large number of characters are named after philosophers – Derrida, Lacan, Husserl, Kristeva, Monad (evoking Leibniz), Berkeley, Deleuze and Guattari. It's certainly the "heaviest" anime series in my list, but well worth the effort.