If you liked
Mawaru Penguindrum
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...then you might like
Charlotte
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Both Charlotte and Mawaru Penguindrum involve teenagers who are somewhat special and get caught up in a lot of supernatural stuff. They center on orphaned brothers who go to great lengths to protect their younger sisters, with the younger sisters being cute and innocent as well as the caretakers of the household. While Mawaru Penguindrum is much more surreal and utilizes a lot of symbolism, Charlotte is shorter and more direct with its premise. However, both anime gave me a similar emotional feeling and if you watch both, you'll definitely see a lot more thematic similarity that I won't go into detail with because of spoilers.
If you liked
Megane-bu!
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...then you might like
Binan Koukou Chikyuu Bouei-bu LOVE!
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Both are colorful, quirky shows involving high school boys in crazy situations. Meganebu! is slighty more based in reality than the magical premise of Binan Koukou, but both series feature similar archetypes.
If you liked
Akuma no Riddle
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...then you might like
Ansatsu Kyoushitsu
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Both shows involve a "special" class of high school students who are given a target to assassinate by a certain time period. While Akuma no Riddle is less humorous and has an all-female cast, Ansatsu Kyoushitsu uses more quirky humor and a target that is virtually indestructible. Both series have a blue-haired protagonist who is level-headed and competent at what they do.
If you liked
Danganronpa: Kibou no Gakuen to Zetsubou no Koukousei The Animation
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...then you might like
Ansatsu Kyoushitsu
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Both shows involve a class of high school students who are suddenly forced into a situation where they have to kill to survive, although in Danganronpa they are killing each other instead of a specific target like in Ansatsu Kyoushitsu. Both have a quirky, nonhuman antagonist and use a weird blend of humor and darker elements. The main protagonist of both series is a typical weak-looking guy who is actually quite perceptive and smart. The art style is also somewhat similar.
If you liked
Tsuritama
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...then you might like
Megane-bu!
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Both series are bright and colorful, with quirky characters. Tsuritama focuses on fishing while Meganebu! focuses on club devoted to glasses, but both have a similar feel. But while Tsuritama combines its whimsical humor with some character drama and a linear plot, Meganebu! is more of a slice-of-life with a few instances of over-the-top drama added purely for comedic effect.
If you liked
Shin Shirayuki-hime Densetsu Prétear
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...then you might like
Mahou Shoujo Madoka★Magica
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Both of these magical girl titles start out light-hearted, but have a darker twist to them as the story progresses. While Madoka has that twist much earlier in the show and Pretear has a slower start, both end up being darker than your average mahou shoujo anime. One of the key ideas in Madoka is also explored in Pretear, though in a slightly different way. This is a spoiler though, so you'll just have to watch them to find out. Overall, both are mahou shoujo series that are more than meets the eye, though Madoka has a much higher art and writing quality and Pretear is still very much a shoujo series.
If you liked
Rinne no Lagrange
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...then you might like
Vividred Operation
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Similar premise of a genki girl living on an island in the future. She likes to help people, and when their town is suddenly attacked by alien robots, she steps up to save everyone.
If you liked
Hachimitsu to Clover
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...then you might like
Sakamichi no Apollon
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Both are about a group of students pursuing their hobbies in the fine arts. Sakamichi is about jazz music, while Honey and Clover is about art. Both have plenty of drama, romance, and humor.
If you liked
Mai-HiME
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...then you might like
Uta∽Kata
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Both are mahou shoujo shows that start out happy, but then become very dark and sometimes brutal. Both show the gradual mental breakdown of the protagonists.
If you liked
Tokyo Mew Mew
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...then you might like
Smile Precure!
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Both are cute, colorful mahou shoujo shows with 5 main protagonists and a cute stuffed animal-type thing. However, Smile Precure is about fairy tales and magic while Tokyo Mew Mew is about aliens and has an environmental undertone.
If you liked
Rinne no Lagrange
|
...then you might like
Medaka Box
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In both series, there is an idealistic young female protagonist who always tries to do what she believes is right, often with no regard to the consequences. Both anime feature a school organization that goes around helping people with whatever they need. Both have some ecchi elements, although it's much lighter in Rinne than in Medaka Box. Finally, both series have supernatural themes, though it very dfferent ways with Rinne being sci-fi and Medaka being some sort of magic.
If you liked
Ultra Maniac
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...then you might like
Tobenai Majo
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Both are traditional magical girl shojo series that seem to focus more on romance and daily life than fighting enemies with magic. Both use the concept of witches and warlocks as magical beings.
If you liked
Marie no Kanaderu Ongaku
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...then you might like
Mahou Shoujo Madoka★Magica
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Both series have allusions to religious ideas, although The Music of Marie is much more obvious with them than Madoka. Both have an interesting art style, even though Madoka is adapted from the anime. If you like a series that starts off light-hearted but becomes dark and mysterious, then you will enjoy both of these.