If you liked
Chihayafuru
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...then you might like
Kono Oto Tomare!
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They both revolve around forming a school club based off of traditional japanese activities with a relatively similar cast of characters that strive to work together to improve their craft. Kono Oto Tomare focuses on traditional koto music while Chihayafuru concentrates on competitive karuta. Their feel and atmosphere are fairly similar. From the animation, colors, tone and character interactions.
If you liked
Higurashi no Naku Koro ni
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...then you might like
Denpa-teki na Kanojo
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Similar atmosphere, many characters are mentally unstable and are very homogenous to the characters in Higurashi and is on the subject of mysterious crimes including murder. You'll probably find something that you enjoy in this anime.
If you liked
Steins;Gate
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...then you might like
Boku dake ga Inai Machi
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Both features the ability to time travel. They also bring up the subject of tragedy and sadness of attempting to go back in time to save loved ones. Steins;Gate does go on a more scientific route when it comes to time traveling while Erased tends to gear towards the subject of crime and mystery.
If you liked
Tennis no Oujisama
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...then you might like
Baby Steps
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The only notable similarity is that they are both tennis animes. Baby Steps takes a more realistic and informative approach while Prince of Tennis tends to go for the more over the top action shounen direction. Also, Maruo (the main character of Baby Steps) shares the same playstyle as Inui which is data tennis.
If you liked
Angel Beats!
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...then you might like
Ano Hi Mita Hana no Namae wo Bokutachi wa Mada Shiranai.
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Both tackle on the subject of tragedy and regrets. Similar tone with some comedic effect.