If you liked
Push
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...then you might like
Kouchou-sensei to Kujira
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While Man and Whale is a Greenpeace commercial about saving whales, and Push is a social satire on consumerism and nuclear warfare, essentially both of them are shorts about preserving our planet that come from very talented directors - Koji Yamamura and Osamu Tezuka respectively. So, if you're interested in the topic, check them both.
If you liked
Hells
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...then you might like
Redline
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Two movies by studio Madhouse, featuring crazy experimental animation, over-the-top action and rock'n'roll drive. In general, both are fun, and if you have already watched the one, you should try the other too.
If you liked
Bastard!! Ankoku no Hakaishin
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...then you might like
Detroit Metal City
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These two anime are comedy OVAs that pay tribute to metal music and feature dual-personality protagonists: one personality being kind & modest, and the other - ridiculously over-the-top & immoral.
If you liked
Ginga Tetsudou no Yoru
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...then you might like
Guskou Budori no Denki (2012)
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-both are movies based on Kenji Miyazawa's stories and directed by Gisaburo Sugii; -both feature antropomorphic cat characters, with the protagonist being a young blue cat who takes a slow-paced journey involving surreal dreamlike scenes, strange encounters and symbolism; -the major themes in both movies are altruism, self-sacrifice and losing someone important, which gives them a pretty serious undertone despite the juvenile looks.
If you liked
Hi no Tori
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...then you might like
Tezuka Osamu no Buddha: Akai Sabaku yo! Utsukushiku
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These anime are based on two famous Osamu Tezuka's manga, featuring plenty of characters and large-scale historical plots revolving around a legendary spiritual entity (Phoenix and Buddha respectively). Besides, both are dramas with quite a lot of deaths.
If you liked
Ookami to Koushinryou
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...then you might like
Otome Youkai Zakuro
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If you look for some romance and cute girls with pointy ears, look no FURther as both of these series have them. Also, they both take place in a historical setting: Medieval European in Spice & Wolf and Japanese Meiji era in Zakuro.
If you liked
Urusei Yatsura 2: Beautiful Dreamer
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...then you might like
Twilight Q
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The second episode of Twilight Q and Urusei Yatsura: Beautiful Dreamer are 80's anime directed by Mamoru Oshii that execute essentially similar scenarios to describe our life as a recurring dream. Both are thought-provoking & surreal.
If you liked
Yami no Teio: Kyuuketsuki Dracula
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...then you might like
Kyoufu Densetsu Kaiki! Frankenstein
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Both are classic B-movies by studio Toei Animation, based on Marvel comics about Dracula and Frankenstein respectively. Both feature similar animation style, weird acting, logical lapses and "quality" English dub.