If you liked
Appleseed
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...then you might like
Kidou Keisatsu Patlabor
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Near future cop series with body suits and plenty of action and comedy.
If you liked
Heppoko Jikken Animation Excel♥Saga
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...then you might like
Animegataris
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Parody series full of references to other anime and only a vague idea of a plot.
If you liked
Jin-Rou
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...then you might like
Kidou Keisatsu Patlabor 2 the Movie
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Two dark political tales involving police forces that are slowly paced. Both by the same director and featuring a similar artstyle.
If you liked
Shoujo Kakumei Utena
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...then you might like
Oniisama e...
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Oniisama e... and Utena share the same themes and the same setting: Upper class high school, the social elite circle, an outsider MC, love drama and its consequences, broken characters. Out of the two Oniisama e... is the more realistic version, while Utena goes fully metaphoric.
If you liked
Hotaru no Haka
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...then you might like
Hadashi no Gen
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Both movies tell the same story of wartime suffering of little children and starvation. Grave of the Fireflies is the more suble one, while Barefoot Gen does not hold back, yet both will make you cry hard over the fate of the protagonist families.
If you liked
Kidou Keisatsu Patlabor
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...then you might like
Taiho Shichau zo
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Two short OVA series from around the same time, featuring the everyday life of Japanese police department with female protagonists. Both series have a similar upbeat slice-of-live mood and excellent animation quality.
If you liked
Shinseiki Evangelion
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...then you might like
Shoujo Kakumei Utena
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The directors go all out with metaphors, artistic shots and cuts. The viewer is left to scramble to follow the plot, but rewarded with deep philosophical questions along the way. While the plot is very different, the similarity of the "feel" of the series and their impact on the viewers is what drives this recommendation.
If you liked
Suzumiya Haruhi no Yuuutsu
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...then you might like
Chuunibyou demo Koi ga Shitai!
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A boy enters high school with the plan to live a "normal" life there. Expect, a wacky classmate has different ideas and pulls his normal life of track. Both series are produced by KyoAni and share the basic setup. The slightly later Chuunibyou also often references Haruhi. It can be thought of as the real life version of Haruhi: How would the whole situation play out if no extra-human powers where involved?
If you liked
Koukaku Kidoutai
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...then you might like
Akira
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The movies share the same setting, Neo Tokyo, and the same cyberpunk aesthetic. In addition, they deal with related questions about what makes a human.
If you liked
Gunslinger Girl
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...then you might like
Haibane Renmei
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You can compare anime by mood or by plot. If you go by mood, Haibane Renmei and Gunslinger Girl are very similar. Both have the slow-moving, heavy-thinking setup that makes you ponder moral questions. The plot, however, could not be more different.
If you liked
Juuni Kokuki
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...then you might like
Tenkuu no Escaflowne
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Both are series in the old-school style of Isekai: The protagists are school girls, they are whisked away to a fantasy world (instead of dying to get there) and the stories are strong on adventure and world-building, but with a good dose of romance.
If you liked
Mugen no Ryvius
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...then you might like
Macross
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Have you ever wondered how a large group of people, stranded on a powerful spaceship would develop if on their own and under attack by numerous enemies? Macross and Mugen no Ryvius give two different answers to that question. One is the uplifting tale of humans coming together, the other the breakdown of society and decent into a dog eat dog world. Common to the two series is the interesting, similar, main storyline, but also the large amount of disbelieve that needs to be suspended to gap the technical plotholes.
If you liked
Akira
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...then you might like
Bubblegum Crisis
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Bubblegum Crisis most likely inspired Akira and both share a common setting: a near future Tokyo turned cyperpunk dystopia. Oh, and motorbikes feature prominently! High points of both are the gorgeous backgrounds, the action sequences and the dark themes. Shared weak points are the lacking characterization and rather straight forward plotline.
If you liked
Hanasaku Iroha
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...then you might like
Sakura Quest
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Given that both series are made by the same studio, the numerous similarities should not be surprising: The story features a city girl surprisingly stuck with a job in a small province town. She has to adapt, make sense of her co-workers quirks, and, of course, win everyone over with her determination and passion. She will be joined by a small group of female colleagues and friends, who form the "inner circle", plus a wider array of some more unique side characters. The same animation quality and realistic style features in both stories. In either case the backdrop is coming to terms with finding a way and purpose in life, while the series is also a love-letter to province life.
If you liked
NieA Under 7
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...then you might like
Kobayashi-san Chi no Maid Dragon
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A hard working female main character of rather stoic demeanor finds herself sharing her flat with an non-human. The series are slice of life, with a good bit of comedy thrown in. Despite the obviously crazy setup of the story (alien freeloader/dragon maid), this background is only ever hinted at, never explored indepth. Instead, the human main character is center to the show and steals it, too. Having no male lead prevents both serious from following romance/harem clichées.
If you liked
Kurenai no Buta
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...then you might like
Tenkuu no Shiro Laputa
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Same director, same time, same animation studio. It should not surprise that both movies are similar. Hayao Miyazaki's love for flying shines through in either case. Especially the scenes among the pirates could be stitched together without a visible seam. The biggest difference comes in the form of the main characters, an older scoundrel in Porco Rosso, a young adventurer in Laputa.
If you liked
Aa! Megami-sama!
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...then you might like
Video Girl Ai
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Two OVAs from the early 1990s where the main plot device is a suddenly appearing non-human, but human looking, girl. Obviously, the surprised male lead falls in love with her. And by the end of the short (5/6 episodes) series, the mood shifts from comedy to drama. The series even straight lift specific elements from each other (looking at you, girl crawling out of a TV). In terms of differences, Video Girl AI is more slapstick-based and has a more involved plot. Aa! Megami-sama has the better production quality.
If you liked
Mai-HiME
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...then you might like
Mahou Shoujo Madoka★Magica
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Mai is the spiritual predecessor to Madoka. All of the themes are given a first try here, even if Mai still shies away from the full deconstruction of magical girls that Madoka performs.
If you liked
Hikaru no Go
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...then you might like
Chihayafuru
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An old-fashioned japanese sport, of sitting in calm poses, presented in a very favorable light, using extensive motion blur for simple movements. A tournament where our hero improves, a long ladder of ranks to reach, from highschool club to japanese masters, the goal of becoming the best. A triangle of love and one of rivalery, unresolved throughout the year, keeping the viewers interest, through tedious explanation of minute rules.
If you liked
Suzumiya Haruhi no Shoushitsu
|
...then you might like
Steins;Gate Movie: Fuka Ryouiki no Déjà vu
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Eerily similar. The quirky main character disappears, people do not remember him/her, the love interest has to search for them, time travel plays a big role. The animation is top. In both cases, you should watch the TV series first.
If you liked
Suzumiya Haruhi no Yuuutsu
|
...then you might like
Steins;Gate
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The main similarity of the two series lies in the main character and their connection to the characters around them. Both Haruhi and Kyouma are eccentric, loud, and drag their friends into untold mysterious operations. And while the friends outwardly complain, they would not have it any other way.
If you liked
Seikai no Senki
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...then you might like
Ginga Eiyuu Densetsu
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Large scale space battles and a focus on building an epic science fiction world are shared points. There is plenty of exposition and calm discussion of tactics. You will also experience the outdated, yet fitting and sometimes beautiful animation style. Finally, both shows challenge the view that democracies are the superior form of government. Note that Seikai no Senki is considerably smaller in episode and character count. It is the sequel to Seikei no Monshou. While a great anime itself, watching Seikei no Monshou first is not strictly needed.
If you liked
Planetes
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...then you might like
Shirobako
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Despite the difference in their setting, both Shirobako and Planetes explore similar topics: starting out in a new workplace, full of new rules to learn, mistakes to make and co-workers to meet. In both anime, the focus is on everyday worklife, not large plots to save the earth from destruction. The enemies are deadlines and broken equipment, not the big bad of the week. You will follow the inexperienced lead through her experiences at the workplace, see her question her purpose in life and, finally, find fulfillment at work.