If you liked
Asobi ni Iku yo!
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...then you might like
Omamori Himari
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The female protagonists of the two anime have cat-like traits. Both are harem anime series.
If you liked
Azumanga Daiou The Animation
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...then you might like
Arakawa Under the Bridge
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They both depict the daily lives of the characters with the emphasis on their randomness.
If you liked
Kimi ga Nozomu Eien
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...then you might like
Bokura ga Ita
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These two romance anime both features love which, at some point, leads to betrayal.
If you liked
Saiunkoku Monogatari
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...then you might like
Densetsu no Yuusha no Densetsu
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These two anime features characters who support a certain person in ruling a kingdom and the hardships they face by doing so. There are lot of bishounens in these, too. And both give us romance, of course.
If you liked
Kiniro no Corda: Primo Passo
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...then you might like
Starry☆Sky
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Both anime are filled with eyecandies --- those are the bishounen male characters. Additionally, both stories are set in a school which is centered in a certain field. In La Corda, the school is a music school where the students play various instruments while in Starry Sky, the school specializes in astronomy.
If you liked
Hakuouki
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...then you might like
Otome Youkai Zakuro
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They have 4 similarities: (1) Both are set in a historic period of Japan. (2) The characters of the two anime both fight mythical creatures (demon in Hakuouki, spirit in Zakuro) (3) Both anime have romance in it, and (4) The male characters of both anime are bishounens.