If you liked
Kage no Jitsuryokusha ni Naritakute!
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...then you might like
Nageki no Bourei wa Intai shitai: Saijaku Hunter ni Yoru Saikyou Party Ikuseijutsu
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Coincidence is king! Both series create rather hysterical scenarios around the misinterpretation of the main characters words. With fanatical fever to make sense of the MC's bullshit, the talented side characters work off what he has to say and just make things work. The world of Kage... is more direct in this kind of comedy around coincidence, but Nageki... is slowly building up the stakes.
If you liked
Mahou Shoujo Madoka★Magica
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...then you might like
Black★Rock Shooter (TV)
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It's hard to explain what the similarities are... But the way they are written, drawn and animated have very similar qualities. Both anime's involve deep emotional stories that are griping. The main themes of always believing in yourself and your friends is also similar. (But they both still have a fair amount of action as well) The most striking similarity however is that the main characters use their timid yet very hopeful and bright personalities to fight the INCREDIBLY sad circumstances that they have to face.
If you liked
Natsume Yuujinchou
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...then you might like
Chihayafuru
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The stories aren't similar at all, the idea behind the anime's are completely different, and the characters have little in common. However both Natsume Yuujinchou and Chihayafuru are very warm-spirited anime. In Chihayafuru and Natsume Yuujinchou you find yourself smiling unconsciously when the main characters succeed at one of there goals or a nice emotional moment happens. The most striking similarity between the two is the inter-character relations. Both characters are able to make friends because of their various skills and personalities and this friendships blossom into strong bonds which I think are the basic foundations which make each of these anime so great. Natsume makes fiends with the spirits that continue to bother him and Chihaya is able to conquer the challenges that face her because of her friends.
If you liked
Gintama
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...then you might like
Beelzebub
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If you liked Gintama's senseless violence and lack of a major plot than you should watch Beelzebub. Beelzebub has more of a plot than Gintama which is based on various 3 to 6 episode long archs, which in no way relate to each other. However all the comedic aspects of the shows are similar. One of the main characters who cant actually do anything is just there to point out whats obviously wrong with the situation. A stupid main character who can be very EPIC when he has his moments.