Another great manga (and anime) title from Rumiko Takahashi.
And unlike a childish acquaintance of yours truly suggested, it is NOT a piece of hentai involving dogs. Ack.

Viz is releasing the manga in the US as Inu-Yasha. This writeup will use the correct romanization.

Inuyasha started appearing on the Shonen Sunday magazine in November 1996. At the time of writing 190 issues of this ongoing series have been released.

The story starts in contemporary Japan, as a girl called Kagome receives the Shikon Jewel from her "superstitious" grandfather on the eve of her 15th birthday. The next day Kagome gets attacked by a centipede demon, who drags her into an old well transferring both of them to the feudal age. Kagome encounters people from a nearby village, who believe she is the reincarnation of Kikyo, a priestess who died 50 years ago fighting the legendary half-demon Inuyasha. As the centipede returns to attack again, Kagome encounters Inuyasha, who is sealed in suspended animation by Kikyo's arrow. Kagome frees the half-canine so he can take care of the enemy, but soon finds out he has a quite different agenda from what she expected.

And this is merely the intro. Instead of spoiling things further I urge you to get your hands to the manga and read it yourselves. In my opinion the honorable artist has outdone herself again. The characters are great, the artwork is near perfect*, the action never stops and the plot never leaves you cold. Inuyasha is naturally a must-have for any Takahashi -fan, but I don't see why it couldn't attract those bored with Ranma & co as well.
Viz comics is naturally running far behind with their English translated versions, but there are fan-made translations around the web for the anxious fans who are unable to read Japanese.

The anime version premiered fall 2000 on Japanese TV, with 3 episodes currently shown. As of now I have only seen the first one, but the series seems quite promising. The plot follows the manga almost 100% identically (although it's too early to say that for the entire show), and the seiyuu sound fine to my ears. I don't have much negative things to say about the animation either, with nice CGI effects to spice up the action. The violence and nudity is toned down from the comic, but who cares? This isn't an ecchi title anyway.

* This is of course subjective. I happen to love Takahashi's "simplified" style.

Update - August 3, 2001

The anime series has been running for over 30 episodes at the moment, and has proven to be quite popular. DVDs have also started to be released in Japan, and I recently grabbed volume 1. It only contains two episodes (later volumes apparently feature 3 per disc) and the extras consist mainly of trailers and a few sketches. Although I like the anime version, I probably won't be buying all of these, at least until a box set is released. A bit too expensive.
As any popular anime title, Inuyasha has naturally gotten its share of merchandise. I have personally only seen the 3 complete trading card sets my friend got, which were quite nice. There's more stuff out there, from keychains to calling cards.

I hate to do this since writeup does not mean reply, but I have to strongly disagree with what microlith is saying. Americans still seem to be under the impression that World == USA. There are a lot of European anime fans out here, and how do we, or anyone for that matter, benefit from having an anime title being shown cut and dubbed on US TV? This is why fansubbing should not (and will not) stop until they've at least released uncut subbed DVDs in the States. But this is a discussion which should take place elsewhere.