Spirted Away or "The Spiriting Away of Sen and Chihiro" or "Sen and the Spiriting Away of Chihiro" was released in America in 2001. I just watched it again and I am on a Miyazaki fix right now.
The IMDB ranks it among the top 50 movies, won the Best Animated Feature at the 75th Academy Awards, and the 6th best animation film.
It is often commented that the film constitutes an allegory on the progression from childhood to maturity, and the risk of losing one's nature in the process. The theme of a character being lost inside a (fictional/different) world if he/she forgets his/her real name is reminiscent of Michael Ende's Neverending Story, where two books with two distinct worlds intertwine. The protagonist of Ende's book, Bastian, slowly enters the world of the book he reads and is threatened to be forever lost inside it if he forgets his real name. Similarly, Chihiro and Haku could forever stay in Yubaba's possession if they forget their real names and consequently their real identities.
The main character's development in the setting could also be seen as a sullen, spoiled and very modern Japanese ten-year-old being forced to grow up when faced with more traditional Japanese culture and manners. Miyazaki himself has said that there is an element of nostalgia for an older Japan in the film.
A separate understanding holds that the film is based on the prevention of greed: those swallowed by No Face were attempting to receive the gold he made. Similarly, compare Yubaba's rich accommodations and interest in gold to Zeniba's rustic home and grandmotherly demeanor. Also, Chihiro's parents' grotesque transformation after consuming too much food not meant for them is another representation of human greed.
One of the strongest themes in the movie is that of environmental awareness. The most obvious examples of this are the river spirit's dramatic and beautiful transformation once he has been freed from the material dumped in him by humans, and Haku's discovery that the reason he cannot go home is that he is the blocked-up River Kohaku.
Miyazaki also refrains from creating any characters with complete ideologies of good or evil, exhibiting all characters with some negative and positive traits in different situations.