If you liked
Kami nomi zo Shiru Sekai
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...then you might like
Yahari Ore no Seishun Love Comedy wa Machigatteiru.
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There is really nothing similar in the plot and little in the style, but hikkigaya and keima are essentially the same person. Both are total outcasts and cynics, but they prefer it that way. On occasion in both shows you begin to realize they both have a heart. Also, both shows have incredibly unsatisfying endings.
If you liked
Kiniro no Corda: Primo Passo
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...then you might like
Uta no☆Prince-sama♪ Maji Love 1000%
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Both UtaPri and Kiniro no Corda are essentially anime based around music appreciation. Kiniro no Corda takes this a little more seriously whereas UtaPri likes to focus more on the comedy, but both really like to delve into how music can be life changing. Also, both mc's begin as novice to music, but through the series begin to grow through their love for it. Both are also an odd sort of reverse harem in that all the pretty bishies fall for your girl, but romance almost never plays a part in the show. Also, both are FANTASTIC
If you liked
Inu x Boku SS
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...then you might like
Kamisama Hajimemashita
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Both feature a very light humor that will keep you cracking up pretty much the whole time. Also, both male leads are fox-spirits that serve your young female lead, superficial perhaps but it had to be mentioned. Both also have the pretty, helpful male leads with the dark past who fall for their mistresses into a relationship that's not socially acceptable for various reasons. Honestly their cut from the same cloth, they have the same flavor and I think fancs of the one will like the other.
If you liked
Special A
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...then you might like
Kaichou wa Maid-sama!
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These animes are largely mirror image, with a somewhat different setting and plotline. Both contain a somewhat flat female lead who is very smart and very strong, but so thick it is hard to believe, who is constantly trying to surpass the male lead (Kei and Usui) who is beyond human level at just about everything. Both rely on a lot of over-the-top humor and animation. I will say that the supporting cast in Special A is better developed and more likeable.