If you liked
Yokohama Kaidashi Kikou: Quiet Country Cafe
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...then you might like
Yuru Camp△
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Both take place around the same area of Japan, around Mt. Fuji (albeit one in a semi-post-apocalypse), and focus very strongly on a quiet, simple existence in a world that might otherwise be chaotic and hectic-- in the case of one, the pressures of a high school life, and in the other, the possible end of the world. They've both got very similar moods and you'll like'em both.
If you liked
Umi ga Kikoeru
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...then you might like
Kimi no Na wa.
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Youth with big dreams in a small town. Growing up and growing apart, flittering back to those memories of the past that grow ever fainter. Art styles that find beauty in the small details of everyday life.
If you liked
Hirune Hime: Shiranai Watashi no Monogatari
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...then you might like
Uchiage Hanabi, Shita kara Miru ka? Yoko kara Miru ka?
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Two films with very interesting and original ideas, executed in baffling and frustrating ways that have a good chance of leaving you annoyed. But they both have some good elements to enjoy if you can look past that.
If you liked
Kino no Tabi: The Beautiful World
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...then you might like
Yuru Camp△
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Kino's Journey and Yuru Camp definitely are two very different shows, don't get me wrong. But they've got a similar quality to them, this nebulous feeling of calmness. One is a post-apocalyptic(ish) fairy tale about an androgynous traveller and their talking bike, and the other is some teenage girls camping around middle Japan, but I can say that you have a good chance of liking one if you like the other. Both shows find beauty in the world in understated, small moments, a kind of tranquility that Japanese animation excels at.
If you liked
Hourou Musuko
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...then you might like
Yagate Kimi ni Naru
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Do you want to watch a show that covers a wide swath of LGBT issues with relative seriousness and delve into numerous different ideas about human identity? Do you enjoy shows that revel in quiet softness and faint, sad smiles? Of course you do, and both Hourou Musuko and Yagate Kimi ni Naru do exactly these things.
If you liked
Mahou Shoujo Madoka★Magica
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...then you might like
Murasakiiro no Qualia
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This is actually for the Anime version of Madoka Magica, plus its sequel movie The Rebellion; I don't recommend the manga version of Madoka because it's an inferior adaptation. Qualia the Purple and Madoka Magica are.... REALLY similar in theme and character dynamics; while the plots are completely different in almost every way, the main character in Qualia is extremely similar to the protagonist of Madoka and they deal with the same concepts of probability vs. destiny, desperation vs. love. The stories diverge significantly in how they approach these themes, but they're interesting companion pieces to one another. Madoka is more focused on its characters and the dynamics between them, while Qualia is concerned more with the protagonist's introspection; despite this, they are both highly entertaining, highly captivating stories. If you enjoy one, you will most likely really enjoy the other.
If you liked
Yuru Yuri
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...then you might like
Yuri Seijin Naoko-san (2012)
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Lesbian-themed slice-of-life madness! Naoko-san is only one episode and is intensely perverted, unlike Yuru Yuri which largely stays away from that stuff, but both are very funny and fast-paced with jokes. If you like one there's a good chance you'll like the other.
If you liked
Shinseiki Evangelion
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...then you might like
Kidou Senshi Gundam 0080: Pocket no Naka no Sensou
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If you liked the harrowing coming-of-age madness from Evangelion, War in the Pocket (written by Gainax co-founder Hiroyuki Yamaga) is another story you'll probably love. It doesn't require much knowledge of any other material, and at six episodes it's not too long either. Gundam is always known for its personal look at the horrors of war, but this one is probably its most emotional effort.