If you liked the Armitage III anime, the Anime-Planet community thinks you'd like:
It is the year 2029, and as many rush to embrace the changes that cybernetic technology bring to mankind, the seedier side of humanity is even quicker to take advantage of it. This series follows Public Peace Section 9, a government organization that plays behind the scenes to stop the worst of these criminals. Join Major Motoko Kusanagi and her team as they take you through an incredibly vivid world filled with plots of such depth and intrigue as is seldom seen.
It should really go without saying, but if you're into cyber-punk animes that just plain rock, make sure you watch them both.
There are some striking similarites between these two; they're both cyberpunk stories with a female police officer as a lead character, they feature plenty of action, both police work and otherwise; cybernetics and androids are common in the setting which gives plenty of opportunities for exploring if technology bridges the gap between the artificial and the organic, humans and machines and what effects this might have on society as a whole.
If one of them interested you for any of these reasons, be sure to check out the other one.
The year is Tokyo 2034, and humans coexist with artificial intelligences known as Boomers. The Branch, a special police unit, has the mission of handling all Boomer crimes. With the help of Basil, the Boomer Rod, the heavy weapons-freak Reiko, the Boomer-expert Bill, and Elza, the Branch must protect people from defective Boomers and investigate why they are suddenly going berserk. The case becomes more complicated when Kimbal finds a mysterious drug during one of the investigations. Mad Dolls, a dreaming hooker Boomer, and unexpected events unfold into a political conspiracy against Boomers and Basil himself!
Both Paraside Dolls and Armitage III are taking place in a cyberpunk world, in which robots and humans coexist. The nature of robots reached a point where they can claim a citizenship like humans, and this question is dealt with through murder cases, and criminal activity.
Armitage III and Parasite Dolls are about androids in a world of humans. In both series you can see a kind of investigations about murders involving robots. Style and plots are on the same level and I think whoever liked one could like the other too.
Hazama is a private detective, who becomes fatally wounded in a run-of-the-mill case. In order to survive, Hazama is tranformed into the legendary cyborg 8Man -- to put an end to the cybernetically-enhanced criminals' wave of crime. But as the death count increases, Hazama soon begins to question how much of his real self is left, and if the emotionless 8Man he becomes is really in control...
What are the differences between man and machine? What defines a soul? Both 8 Man After and Armitage focus on finding the answers to these questions for themselves while blowing things up of course. If you liked one you'll like the other.
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.
Armitage is cyberpunk defined - it's slick, sexy, gritty, and set in a post-apocalyptic world; oh, and did I mention the lead character is a robot? Animatrix is undoubtedly much more gorgeous, being made many years in the future. Though this might seem to be a strange recommendation to some, I strongly feel that the type of person who likes Animatrix's grim and gorgeous look at a world overrun by machines will love the cyberpunk elements of Armitage, and vice versa.
When freelance reporter Sybel finds out about a potentially hot scoop involving a crashed military plane, she has no idea what she is about to get herself into. The plane, she discovers, was carrying two top-secret prototype robots known as M-66. The problem? The mission of these programmed killers is to assassinate the granddaughter of their creator. Now, Sybil must race against the clock to help save this innocent girl's life, while protecting her own...
Both of these are old cyberpunk OVAs, involving corruption in government, deadly robots, sexy girls, and an adequate slice of action. Armitage III has more when it comes to story and characters, but Black Magic M-66 one-ups it on the action quotient.