 If you liked
Sen to Chihiro no Kamikakushi
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 ...then you might like
Mononoke
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Despite their disparate art styles, Spirited Away and Mononoke have very similar atmospheres. This in part stems from more traditional Japanese influences (themes centering around Shinto, social structure, and other worlds, etc.) mixing with more contemporary aesthetic and narrative features of anime. Also, while I am sure there are more natural comparisons, the fact that these are both so strong makes the watching experience hard to equal in both cases.