Ooh, nice topic. I love an excuse to rant.
Number one thing for me would have to be the characters. For a series to stand out to me, it has to have great characters--characters that are interesting and funny and mysterious and easy to relate to--and the cast of Inuyasha is definitely up to the task, as much so as any other anime cast I can think of... maybe even more. To modify a quote from Lord of the Rings, "You can learn all there is to know about their ways in a day, and yet after a hundred episodes, they can still surprise you."
They're all simple, more or less, and yet they have so much
depth. Inuyasha's a brash hanyou who won't hesitate to pick a fight, and yet beneath all that he's really a sweet, sensitive guy who just happens to have had a really tough life. (Such is the profile of many a great anime hero... but hey, the formula works.) Kagome's a naive schoolgirl, but she's got heart, and there's more to her than you'd expect (definitely more than your typical anime schoolgirl heroine). Miroku's a lazy pervert of a monk, and yet he's the most intelligent and observant of the group, and probably the second most capable after Inuyasha. And so on and so on. I never get tired of them.
Number two is definitely the epic scale of the story. I like more episodic series like Trigun and Cowboy Bebop just fine, but the epic series are the ones I get
addicted to. I love to watch the characters develop as they go through so many different trials. I love following along the plot as it moves forward--and backward--and goes through all sorts of twists and turns. I love seeing the characters' romances move along the same winded path, even when it gets frustrating. It just makes it all the more satisfying in the end when, hopefully, we get a happy ending. To me, long, epic stories are the best stories, and Inuyasha is one of the most enjoyable I've seen in a long time.
And
number three, last but not least, is the bishounen. Oh, I'm sure I'd love Inuyasha, Miroku, Sesshoumaru, and everyone else even if they
weren't outrageously hot... but as an admittedly shallow fangirl, I'm sure not complaining.