It's not easy to narrow down to just 10 anime and rank them, and there are many others that are worth watching outside of this recommendation list, of course.
Fate
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Fate/Stay Night, based on the game for Windows, was released in 2006 as the first season of the Fate series.
Inuyasha
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Inuyasha (犬夜叉) is a popular manga published by Weekly Shnen Sunday, which consists of 56 volumes altogether, and has been adapted into an anime.
Steins;Gate
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Quite a few anime lovers look on Steins;Gate (シュタインズ・ゲート) as the best anime in recent years.
Detective Conan
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The high school detective Shinichi Kudo is transformed into a kid by a poison named APTX-4869
Fullmetal Alchemist
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Fullmetal Alchemist, which is abbreviated to Hagaren in Japanese, is a well-known Japanese sci-fi anime worldwide.
Dragon Ball
Many anime fans associate the most famous action anime with Dragon Ball (ドラゴンボール), which began airing in 1984.