Total Recommendations: 2
If you liked
Sen to Chihiro no Kamikakushi
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...then you might like
Momo e no Tegami
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They both have the same kind of idea; a young girl moving to a new town against her own will while befriending spirits along the way. Both involve saving parent(s).
If you liked
Gakuen Alice
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...then you might like
Kodomo no Omocha (TV)
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Kodomo no Omocha and Gakuen Alice both have VERY similar characters. Natsume is a lot like Akito, and Mikan is a lot like Sana. The relationship between the two is also VERY similar. Kodomo no Omocha doesn't involve supernatural powers though. Other than that, they're REALLY similar.