Unlike many American cartoons, which are known for being episodic, most anime feature continuous plots. Though continuity is one of the medium's strengths, anime with standalone episodes can be just as engaging as any Death Note or Naruto. Unlike continuous anime, standalone episodes offer a great way to avoid the pain of cliffhangers when the next episode just isn't available. Nothing's more painful than having to wait a week when you don't know if your favorite character is going to survive.
Standalone episodes can also be a great tool for getting your significant other, parents, or other reluctant loved ones to try out anime. Rather than force them through a 10-episode arc before they understand a series' value, you can give them a full story in less than half an hour.
Anime with standalone episodes such as Mushi-shi and Hell Girl technically follow overarching storylines, but they typically take a backseat to whatever action happens in an individual episode. They even pop up in shows like Gintama and Ghost in the Shell: Stand Alone Complex, which feature a combination of longer arcs and stories that end after a single episode. There's no one way to structure an anime, and these unique shows prove it.
Cowboy Bebop is probably the best-known example of an anime with multiple standalone episodes. While this legendary show follows an overarching plot that reappears over the course of the series, individual episodes contain their own unique stories. Whether it's a character study of a Bebop crew member, an episode where they must defeat a chess master, or an episode where they take spoiled mushrooms, each one tells a different but no less engaging story than the one before or after.
Samurai Champloo follows two samurai bodyguards as they help a former waitress, Fuu, search for the mythical "samurai who smells of sunflowers." While an overarching plot centers around that search, most episodes focus on a unique adventure. Sometimes, it involves epic sword fights, and sometimes it involves getting high off of a field full of burning plants. Whatever it happens to be, an episode of Samurai Champloo always one hell of a ride.
Although the human face of Mushi-shi is Ginko, a man who deals with problems created by mushi, the true protagonists are the mushi themselves. These creatures, the building blocks of life capable of bestowing a user with psychic powers or forming living rainbows, make the world of Mushi-shi fascinating. Thus, it makes sense for each episode to introduce a new mushi with unique features, rather than dwelling for a long time on any single one.
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Sometimes referred to as as the "standalone" and "complex" installments, Ghost In The Shell: Stand Alone Complex features both episodes that do result in a story arc, and episodes that resolve their stories in one take. Despite not adding to the overall plot of the anime, these installments are mini cinematic masterpieces that contribute greatly to the dark, gritty mood of the overall series.