Total Recommendations: 3
If you liked
Fruits Basket
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...then you might like
Kamisama Hajimemashita
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They both have a similar atmosphere and sense of humor - probably because they both share the same director: Daichi Akitarou.
If you liked
Tengen Toppa Gurren Lagann
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...then you might like
Giant Robo the Animation: Chikyuu ga Seishi Suru Hi
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If you loved Gurren Lagann, I guarantee you'll love Giant Robo. Both feature wonderfully over-the-top "hot-blooded" action, GAR characters, epic scope, and excellent production values, especially in the case of Giant Robo, which took six years to finish animating the 7 episodes.
If you liked
Fantastic Children
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...then you might like
Boku no Chikyuu wo Mamotte
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Both deal with reincarnation within a fantasy/sci-fi setting as their primary premise.