 If you liked
Mononoke Hime
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 ...then you might like
Seirei no Moribito
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Plotwise both are about a prince who's going on an adventure to fight a curse and stand up to his fate.
Also the fantasy world's setting is similar: These are times when men fight between each other but also nature that they don't understand. Anime touch the subject of spiritual beings, demons and moral problems of humans who don't treasure life.
Both have the same feeling to it, and both are about someone running away from his home for the same reason which is being cursed.
Moving story, motivated characters, well-crafted fantasy setting.
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Recommended by Encephalon
Both are great epics, both are about the importance of respecting nature, the coexistence of the world of humans and the world of spirits, and both are about the encounter of two characters from very different worlds, who have a choice to make between fighting (aka destroying life even if it is to protect something) and being nurturing (aka perpetuating life).
Also the visual style of both has a lot of volume and matter.