If you liked
Sen to Chihiro no Kamikakushi
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...then you might like
Hottarake no Shima: Haruka to Mahou no Kagami
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It will be actually one-sided recommendation - most people at least heard of Spirited Away. Hottarake no Shima, however is very underrated in my opinion. Just like in Spirited Away, we have a young girl who wents into the world of magic and encounters it's strange inhabitants. Both movies have beautiful visuals, Hottarake no Shima, however, is CG while Spirited Away uses the traditional animation. Even if you're not a fan of CG, give it a try, because good anime movies are becoming a rare thing. Especially family-friendly ones.
If you liked
Uchuu Kuubo Blue Noah
|
...then you might like
Uchuu Senkan Yamato: Fukkatsu-hen
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You can basically count Blue Noah as a spin-off of Yamato saga. The titular ship also makes it's appearance in Uchuu Senkan Yamato: Fukkatsu-hen. If you liked Yamato, you might want to check out the story of Blue Noah and vice versa. The main difference lies in the fact that Blue Noah fights on and under the sea during most of the episodes, while Yamato is cruising through the space. Both ships are also the only hope of the humanity during the alien invasion.
If you liked
Ookami to Koushinryou
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...then you might like
Dantalian no Shoka
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Both series have this calm, soothing atmosphere and take place in older Europe. There are many supernatural elements, including main heroines of both stories. Dantalian no Shoka is more action-packed with little horror here and there, while Spice and Wolf is actually calmer, with more focus on solving problems by persuading.
If you liked
Berserk
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...then you might like
Le Chevalier D'Eon
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Swords, demons, great graphics, violence... Both mangas offer almost the same. Le Chevalier D'Eon is shorter, but enjoyable, while Berserk is known for it's long, epic story. In both series the protagonists are hunting for traitors to avenge the past.
If you liked
Simoun
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...then you might like
Sentou Yousei Yukikaze
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Both of them are about war, dogfights and personal problems. The main difference lies in the fact that Yukikaze is SF and Simoun is more like Steampunk, but if you'll like one of them at least a bit, you'll most likely enjoy the other one. Both series also have a wonderfull Soundtracks, fitting the events in the air and on the ground. Simoun is also known as a yuri anime, but it's not really like most of the yuri series.