If you liked
MM!
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...then you might like
Kami nomi zo Shiru Sekai
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Both have a main character who can be seen as being a "god-like" figure---Mio being a self-proclaimed god, while Keima obtains his name as the "God of Conquests" from people on the internet. Whether willingly, or reluctantly, these 2 gods help out others in their daily lives by solving, or in Mio's case "trying" to solve, their problems. Both are very enjoyable shows overall.
If you liked
Bakemonogatari
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...then you might like
Medaka Box
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Both series are written by Nisio Isin. However, the stories are quite different as well as the art style. In Medaka Box, the story revolves primarily around the antics of a student council who uses a suggestion box to get suggestions from the student body on how to improve the school, or simply to get help with things they couldn't accomplish/resolve themselves. The art resembles your typical anime style drawing (big eyes, abnormal hair colors, flashy uniforms, etc.). Conversely, in Bakemonogatari the story is heavily based on dialogue and is narrated by its male protagonist; it focuses on several females to whom which he helps to rid of supernatural creatures that have caused trouble to them in one way or another. The drawing is more serious and detailed than in Medaka Box.
If you liked
Higashi no Eden
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...then you might like
Mirai Nikki (TV)
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Both series, through the use of cell phones and knowledge, allow for a total of 12 individuals to compete in a survival game. In Mirai Nikki, the objective of the game is to destroy everyone else's diary, or simply kill them, until there is only one person left standing. This final person, by winning the game, is granted the title of god in the place of Deus ex Machina, who is on the verge of death. While, in Higashi no Eden, the objective of the game is for the participants to "save" Japan by using the 10 billion yen that is on their phone. Both series are great and will leave you in awe.
If you liked
Meitantei Conan
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...then you might like
Gosick
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Both series are about mysteries/cases which are ultimately solved by the protagonist, who are both highly intelligent people who possess a keen eye for details. Most cases in Detective Conan can be solved pretty effortlessly, while in Gosick they are more difficult causing you to think more. However, no matter the level of difficulty of the cases, they're always pulled off in a unique & clever way so that even if you know who the culprit is you are still baffled as too how they managed to pull it all off in the 1st place. Also in both series, although the protagonists solve the cases all the credit goes to someone who couldn't solve a case for their life. Both series are really amazing in their own ways, so I recommend you check them both out.
If you liked
Basilisk: Kouga Ninpou Chou
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...then you might like
Romeo x Juliet
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Both are tragic love stories that involve 2 star-crossed lovers whose families loathe one another. Thus, making it utterly impossible for them to be in a relationship without either side holding true to the phrase "where civil blood makes civil hands unclean."
If you liked
Tennis no Oujisama
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...then you might like
Kuroko no Basket
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Both are amazing sports anime, although they do have their differences. The character personalities clearly differ. For example, the main character of "Kuroko no Basket", Kuroko presence goes unnoticed most of the time, he's polite and he doesn't have a natural talent for playing basketball. While the "Prince of Tennis" main character, Ryoma is quite hard to miss, has a natural talent for playing tennis, and is cocky, often shown by the way he taunts players with his catch phrase "mada mada dane." Although, both main characters differ, they are the same in the sense that they both have a love for the sport that they play. An obvious difference in the 2 shows is that their both playing completely different sports (one being tennis, the latter being basketball), but even though they both follow a story line consisting of 2 very different sports, both series allow for the viewer to bond with the show and come to love the sport that's being played as well. If you love predominantly sports based anime's like then you should check out these 2 anime's.