If you liked
Bungou Stray Dogs
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...then you might like
Trickster: Edogawa Ranpo "Shounen Tanteidan" yori
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A group of teenagers with special powers are in a group, helping people from the city by taking on jobs that such as investigations, bodyguards etc. The main character from both anime have a problem with their self-identity and how their powers are used (they both fear themselves and the prospect of their powers hurting others), and are led by a more experienced and "wiser" mentor. Both shows have a similar atmosphere and pacing as well, being very arc-based. If you enjoy one, it is likely you'll enjoy the other!
If you liked
Boku dake ga Inai Machi
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...then you might like
Re:Zero kara Hajimeru Isekai Seikatsu
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Similar themes. The main character goes through the same timeline many times trying to save people and to set things right. Both of these shows have amazing cliffhangers and great art, and you'll watch one episode after another. The only difference would be that Re: Zero is set in a fantasy world with different races, magic and creatures, while Boku dake ga Inai Machi (Erased) is set in a world similar to the real one we live in. If you enjoy one, you'll likely enjoy the other, though.
If you liked
Mahou Shoujo Madoka★Magica
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...then you might like
Charlotte
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Both of these shows explore the realm of saving people (that's all I can without spoiling). The love between each of the characters is definitely and visibly what drives them. Both of these show also explore the duality of hope and despair, although Madoka Magica does it on a much more contrasting manner. The music of both anime is quite amazing, and although the art style is different, both are refreshing in their own ways (with Madoka being more abstract and Charlotte being more "normal"). If you enjoyed one, chances are you'll enjoy the other!
If you liked
Gosick
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...then you might like
Hyouka
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Both of the series are about a detective character (Oreki in Hyouka; Victorique in Gosick) solving mysteries that are usually inquired by another friend. Hyouka and Gosick function in small arcs, where one mystery passes, then another comes. However, Gosick definitely has more of an overarching story and seems to connect between the arcs (not to mention the big romance part of it) while Hyouka appears to be more fragmented (and barely any romance). The Setting is also different: Hyouka is mostly in the highschool, while Gosick is set in the entire kingdom. Despite the differences, both series does an excellent job with the mysteries, making them incredibly... addictive to watch (not to mention the amazing graphics as well). If you liked one, you'll probably like the other.
If you liked
Shingeki no Kyojin
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...then you might like
Akame ga Kill!
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The overall atmosphere in both anime are very similar-- both about a shounen boy fighting for something that he wants/believes. Both series are fairly bloody, so if you enjoyed that aspect in one anime, then you will probably like the other. These anime also both have a pretty dark/despair feel to them; death, after all, is not a light subject. Akame Ga Kill has a big cast (Nightraid) and does a good job on focusing on each of the characters, while Attack on Titan also has a big cast from the different corps, it tends to focus more on the main three characters. Another difference is that the antagonists in AGK are human (in the bare minimum of the word), while in AoT they are giant man-eating titans. All in all, if you enjoyed one series, you will most likely enjoy the other.
If you liked
No Game No Life
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...then you might like
Mahouka Koukou no Rettousei
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Both of the protagonist are OP in their own ways and are geniuses beyond comprehension, and both have intimate (maybe even more than that) relationships with their little sisters. A good bit of action is seen in both anime.
If you liked
Ano Hi Mita Hana no Namae wo Bokutachi wa Mada Shiranai.
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...then you might like
Kokoro Connect
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Both of these animes focuses on the bonds between the group of characters that you'll probably love, and both are about a sudden "surprise" in their lives, although Kokoro Connect was cut into many different arcs. They have just too many similarities, such as the animation. Not to mention that they both deal with the "supernatural," although again, Kokoro Connect gives much more of that feeling than Ano Hana If you liked either Kokoro Connect or Ano Hana, give the other one a try, you won't regret it! :)