If you liked
Rainbow: Nisha Rokubou no Shichinin
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...then you might like
Deadman Wonderland
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Both use a Prison setting. Rainbow is based in a realistic setting, set in the 1950s and following the lives of young criminals. Deadman Wonderland is more science-fiction, set in the future and a prison that serves as an amusement park. Both series have a dark atmosphere that stems from their location.
If you liked
Noein: Mou Hitori no Kimi e
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...then you might like
Sora wo Miageru Shoujo no Hitomi ni Utsuru Sekai
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What struck me about Munto is how extremely similar it is to Noein. A young girl is sought out by people from another time and space because she has an important power that will save their world from destruction. The fact that the opening artists are the same is just an eery start, the characters, concept, mood, art style, animation, the setting, etc. all share lots of parallels with eachother. Obviously there are key differences between the two series, but it's definitely worth checking out the other if you enjoyed either of these series.
If you liked
Naruto: Shippuuden
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...then you might like
Tetsuwan Birdy Decode:02
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Episode 87 specifically of Shippuuden features Shingo Yamashita, who does most of the action for Birdy 02, as well as other key animation scenes. If you enjoy his fight animation, you should check out his other stuff.
If you liked
Kannagi
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...then you might like
Tetsuwan Birdy Decode:02
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Both made by A-1 Pictures, they feature a similar type of quirky, lifelike animation in their first episodes. If you enjoyed Shingo Yamashita's animation, you may want to watch his other involvements. Obviously, Birdy has more action, whilst Kannagi is more realistic.
If you liked
Shigofumi
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...then you might like
Tegamibachi: Hikari to Ao no Gensou Yawa
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The plotlines are very different, but the two series share the theme of Postal services, and there's a similar style with Uniform design, letters, and exploring the stories of characters that the protagonist meets.
If you liked
Jungle wa Itsumo Hare nochi Guu
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...then you might like
Kemeko Deluxe!
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Both have some similar staff, as well as sharing the same crazy style and weird brand of humour. If you liked one, you should try the other.
If you liked
Tokyo Majin Gakuen Kenpuuchou: Tou
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...then you might like
Shikabane Hime: Aka
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A spooky atmosphere, buddhist culture, zombies, action. Worth checking out if you liked the other.
If you liked
FLCL
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...then you might like
Kemeko Deluxe!
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It's got the obvious elements, such as "boy meets alien girl", but it also has other similarities such as the wacky robot designs, the boy has a strange power in his head, and it's fast and crazy pacing, as well as having some hilarious moments. There are some obvious parallels between the two.
If you liked
Kekkaishi
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...then you might like
Soul Eater
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Nobody seems to have mentioned the fact that the soundtracks are done by the same composer - Iwasaki Taku
If you liked
Ouran Koukou Host Club
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...then you might like
Soul Eater
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Soul Eater uses a similar style of humour to Ouran, and this is due to the same staff from both series being part of the team working on Soul Eater. Both series are by Studio Bones.
If you liked
Eve no Jikan
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...then you might like
RD Sennou Chousashitsu
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Real Drive sometimes focuses on Androids, especially characters such as Holon. Eve no Jikan is a series that centres on humanoid androids and their place in modern society as well as their own desires, and occasionally some parallels can be seen. Eve no Jikan is worth a watch if you enjoy the Android aspect of Real Drive or any other similarly themed anime.
If you liked
Innocent Venus
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...then you might like
Code Geass: Hangyaku no Lelouch
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Both share very similar aspects. The mecha used in IV are fairly similar to the Knightmares of CG in their size and the way they move. It shares a similar theme of rebels rising up against a government, and there are many other obvious similarities along the way. IV is of course, much shorter than CG, but if you liked either anime then you might like the other
If you liked
Mushishi
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...then you might like
Natsume Yuujinchou
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Although not similar in the aspect of Japanese Youkai, Mushishi still has good Japanese environments and the obvious feature of spirits that can only seen by certain people. Not many blatant parallels can be made between the two, though there's a high chance that anyone who likes Natsume Yuujin-Chou will like Mushishi.
If you liked
Last Exile
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...then you might like
Bounen no Xamdou
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Last Exile and Bonen no Xamdo share a similar sort of flying-ship style, as well as the broad sky travel theme in general. There are also a few scenes that bear some similarity to Last Exile's universe, such as the group of white-haired children.
If you liked
FLCL
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...then you might like
Tetsuwan Birdy Decode
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Birdy and FLCL both share a few characteristic, such as the similar bright art and animation style, and the fast-paced crazy action. They both also involve a fairly cynical male protagonist meeting a hot-blooded alien woman.
If you liked
Koukyoushihen Eureka Seven
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...then you might like
Bounen no Xamdou
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Bonen no Xamdo has the same character designer as Eureka Seven, as well as sharing similar animation styles and mecha themes. Both anime are created by Studio Bones.