I am surprised One Piece fans are so oblivious to InuYasha's popularity, since the fanatisism in regard to both Anime are both cult-like. InuYasha is almost, virtually, the "cultural" counterpart of OP.
Ahem, a short dissertation, by Terek.
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InuYasha was the product of Takahashi's intensive urge to create an epic "mythology' manga, as she grew bored with Ranma 1/2 to the point of having a increasingly noticeable decrease in quality of the later chapters. This is a fundamental problem for all manga-ka; if one loses interest in creating a series, the series starts to suck. Ergo, Oda must be the biggest OP fan in existence.
Using her Ranma 1/2 formula, as well as basing some characters on Ranma 1/2, Takahashi created a cross-genre (Action/Comedy/Horror/Fantasty) Anime about a forlorn relationship. If you watch the first eighty or so InuYasha episodes, or the first twenty volumes of manga, the story makes much more sense and is cough coherently distinctive. It's actually fairly interesting.
The problem occurs when Takahashi ran out of ideas, got bored, or whatever; InuYasha "jumped the shark" in the manga at volume twenty, meaning that the next twenty volume are virtual filler. The Anime, which had to make a stretch in the first place to lengthen episodes (as Takahashi's mini-arcs could be summarized in a single episode) became utterly slow. That's where the Anime is currently on Adult Swim.
In regard to popularity, people have not forgotten the "excellent dub" days of Outlaw Star, Gundam, Dragonball, Big O and Tenchi Muyo. Climates have changed, and more younger viewers are watching shows than older ones later at night; hence, more childish dubs, like OP and Naruto, center around primetime, while older stuff for mature audiences are pushed back. InuYasha has a very good dub, harkening back to the "glory" days of Toonami, as well as having a setting. There are a great deal of "Japanophiles" in America, whom adore the country's culture in such a regard that they are, quite literally, fantatics. This also expains the popularity of Kung-Fu movies anre Naruto; they're foreign, and give a sense of foreginess. The world is is gaining a cultural identity of its own as corporations merge countries together (not literally), so people feel more constrained and lose their primeval sense of wanderlust. People travel because they want to explore; those who lack resources to physically explore must do so through the only mediums they can. Why else do so many people use blogs, to pour their souls into the Internet? They're socially isolated in their own lives, and are started for attention; just like others are physically isolated, and starve for the carefree life of adventure.
Honestly, if given the opportunity, what person on this board would not chose to live the life of Luffy?
On a final note, InuYasha is not on Toonami for two reasons; strong language (though this can be toned down), and one violent scene (InuYasha was pinned to a tree). That's it, nothing else; one could easily lessen any other offenses in the series.