If you liked
Higurashi no Naku Koro ni
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...then you might like
Yojouhan Shinwa Taikei
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Both of these shows feature time loops where the same plot is acted out, taking a different turn each time, and frequently overlaps, with things being told slightly differently. Higurashi is a lot more bright colors and slapstick humor, whereas Tatami Galaxy is somewhat darker humor, with less emphasis on little kids killing each other and laughing.
If you liked
Bamboo Blade
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...then you might like
Angel Beats!
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These shows are alike in a lot of ways. Both involve clubs, and have some fighting.
If you liked
Shinseiki Evangelion
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...then you might like
Narutaru: Mukuro Naru Hoshi Tama Taru Ko
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Both have plots about little kids taking control of powerful mechs (eva) or dragons (narutaru), and with all their psychological problems, a lot of things go wrong. The main characters of each are both cowards who never want to fight, and their allies are a depressed suicidal girl and a manic murderous girl. Comes complete with "Psychological" label.
If you liked
Hoshi no Koe
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...then you might like
Top wo Nerae! Gunbuster
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Similar stories where time-space distortion draws a young military girl and her classmates far apart from one another. Both deal with the uncertainty of knowing what's become of those you're separated from, and how, though living in separate worlds and aging at different rates, in the end, you're still the person your friends always knew.
If you liked
Aria the Animation
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...then you might like
So Ra No Wo To
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Plotwise: Both shows are about a main character being trained by a superior, and her interactions with the new world around her. Characters: Both are primarily female casts, and every character in Sora No Woto bears a resemblance to a character in Aria. Also, where Aria has cats, Sora No Woto has an owl. Setting: Both take place in imaginary worlds around cities where the people and land has a rich history and traditions. The difference here is that Sora No Woto has a wartime setting, where Aria does not. Artwork: Beautiful backgrounds and landscapes, stunning visuals all-around.