If you liked the Eve no Jikan Movie anime, the Anime-Planet community thinks you'd like:
Witness the true beginning of the Matrix: how men created the machines and how those machines stood up against their masters, and the effects of the great war that waged between them, which in the end led to the fall of mankind. Watch the ship Osiris and its efforts to warn the remaining humans of the imminent attack; follow a champion who happens to break free from the Matrix; explore the exploitation of a glitch in the overall system; observe the story of the Kid and how he was found by Neo; travel with an investigator who tracks the well-known hacker Trinity; and learn the secrets of the Matrix in other wondrous ways.
You will like one if you like the other, both involve Sci-Fi aspects as well as machine sentience, where Animatrix emphasises the worst possible outcome being the war between man and machine, Time of Eve focuses on the relationships between man and machine if machines were able to achieve free will.
The year is 2179: humans and robots have colonized Mars. A newer Third-Type robot has been designed to interact undetected in human society. That is, until a man named D'anclaude discovers their secret and starts a movement to wipe them out. Armitage is a Third-Type that works for the police with her partner Ross, and now these two must rid the planet of D'anclaude and his evil plans.
Both of these movies deal with the relationship between androids and humans. The humans begin to question whether androids are safe to live with. The stories examine what it means to be human, and the human-traits shared by machine. Can these two beings co-exist and share emotions? Armitage is more action-centered, but there is definately a link between these two anime movies.
Having failed to earn admission to a university, Hideki Motosuwa has moved to the big city, determined to study his hardest for next year's exams. However, an unusual distraction presents itself one unsuspecting day in the form of Chii, a robotic young girl that has been discarded in the trash. In a world where an increasing number of people turn to these 'persocoms' for company, the bonds and limits of human relationships are tested as flesh manages to fall in love with the machine itself...
Both Eve no Jikan and Chobits deal with human x AI (or more exactly android) relationships. Eve no Jikan is more serious, on the other hand Chobits has some comedy and fanservice in it. None the less, if you thought one of those was interesting, than you should give the other one a try.
A mysterious new hacker known only as the Puppet Master threatens to create chaos, erasing and rewriting the memories of his victims: humans who have cast away their physical body to become cyborgs. Is he an evil genius, or could he signal the beginning of a new age in the relationship between man and machine?
Both Eve no Jikan and Ghost in the Shell deal with the possibility of androids having mind of their own. While the style differs greatly both movies are quite interesting. If you like such sci-fi themes, you should definitely watch both of them.
A young woman quietly falls to the earth, escorted by a solitary crow. This sort of dream, as many other before have dreamed, comes just before being reborn as a Haibane, a charcoal-winged angel. On the outskirts of the walled-in city lies Old Home, a haven for Haibane to study, live, and learn, while waiting for their chance to ascend to the heavens and escape the confines of their new world. Rakka is the newest inhabitant of Old Home who wants nothing more than to remember her past and discover the secrets of her kind. Together with Reki, Kuu and plenty of other new friends, Rakka will laugh, explore, and search for the meaning of their existence in the process.
Both of these shows are totally amazing. More concretely, both Haibane Renmei and Time of Eve are slow-paced, dialog-driven and concentrate mainly on the development of characters and relationships. The depth of the characters in each show is complemented by the detail of the world-building, resulting in a highly engaging experience.