Inuyasha Movie 1
The first Inu-Yasha movie was released in Japan in December of 2001. It's called "Inuyasha the Movie: "Toki wo Koeru Omoi" [directly translated as "Feelings That Transcend Time", but promoted as "Affections Touching Across Time"] is a beautifly animated and writen story about the gang fighting an ancient moth-like demon.
Inuyasha Movie 2
The second movie, "Kagami No Naka No Mugenjou" ["The Castle Beyond the Looking Glass"] was released in Japan in December 2002. I have yet to watch this one, it was released on Japanese DVD in August of 2003.
Inuyasha Movie 3
The third movie "Tenka Hadou no Ken" [The Sword of World Conquest] screened December 20th, 2003.
Toki wo Koeru Omoi : Inuyasha the Movie (1) Information :

Story Line:
300 years in the past, before the sengoku jidai, A demon named Menomaru's father attacked Japan. Inuyasha's father defeated them and Menoumaru's father was sealed up. But, that seal has now been broken and Menoumaru has been revived. Now he's after the power of the Tetsusaiga in order to rule the world. Kagome fights Inuyasha, Kirara attacks Sango, crazy stuff, huh?
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This Movie supposedly takes place around episode 38 or so, before Sesshoumaru gets Tokijin and before things take a slightly crappy turn in the Naraku department. It has nothing to do with the plot of the manga or the anime, but works timeline wise. Also, the movie team consulted with Takahashi-san when creating it. That's always a plus.
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As for the issue of the translation of the title, yes, "Toki wo Koeru Omoi" translates to "Feelings That Transcend Time", but it was promoted in Japan as "Affections Touching Across Time", as you can see in the image scanned from the back of the movie program above.
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I love this movie. It is quite long for an anime movie of its type, and well animated to boot. The story is believable, and Naraku doesn't show, so how can you go wrong? Looking for a copy before it gets released by Viz? Try Ebay.

MAIN STAFF

Original Story: Rumiko Takahashi
Director: Toshiya Shinohara ( The Boy Who Saw The Wind : Animation Director)
Scenario: Katsuyuki Sumizawa( Gundam Wing )
Character Design: Hideyuki Motohashi ( Ayashi no Ceres ) Yoshihito Hishinuma (Turn A GUNDAM, Record of Lodoss War )
Music: Kaoru Wada
Sound Director: Yota Tsuruoka

Kagami No Naka No Mugenjou [The Castle Beyond The Looking Glass]: Inuyasha the Movie (2) Information

Naraku is defeated! But then, a figure from Japanese mythology, Kaguya-hime decends from the moon and tries to take over the world. Since one of the items needed to bring her back is the fire-rat coat Inuyasha wears, the gang gets drawn into saving the world, again. Unfortunatly, a funny appearance of one of Houjou's ancestors and an all-too-brief kiss scene cannot save this movie from the shadow of the first movie.

Played in Japanese theatres 12/02
Promo-posters for the 2nd movie obtained from the Nihon TV movie site

Tenka Hadou no Ken [The Sword of World Conquest]:
Inuyasha the Movie (3) Information

According to Anime Mikomi - Inuyasha and Sesshoumaru fight in an attempt to gain control of another sword commissioned by their father called the Souunnga. With this sword, the owner will be able to rule the world. Also, the secret behind Inuyasha's birth is supposed to be revealed.

Hit Japanese theatres 12/20/03 More Information to follow.
Promo-poster for the 3rd movie obtained from the Nihon TV movie site