Joe Hisaishi has been Japan's foremost composer of film music in the last two decades. Best known for his music for the films of Hayao Miyazaki and Takeshi Kitano, he is one of my favorite contemporary composers, not only for his mastery of the musical craft and his bold eclecticism, but also for the way the music is perfectly fitted to the image. He is far above, in my opinion, many overrated film composers such as John Williams and James Horner. Here are links to pieces from the many soundtracks he has composed:
Joe Hisaishi meets Kitano Films
Sen to Chihiro no Kamikakushi (Spirited Away)
Studio Ghibli Songs (#1-4, #16 composed by him)
Tonari no Totoro (My Neighbor Totoro)
Kaze no Tani no Nausicaa (Nausicaa of the Valley of the Wind)
Mononoke Hime (Princess Mononoke)
Hauru no Ugoku Shiro Image Image Album (Howl's Moving Castle Image Album)
Hauru no Ugoku Shiro OST (Howl's Moving Castle OST)
Majo no Takkyuubin (Kiki's Delivery Service)
Tenkuu no Shiro Rapyuta (Castle in the Sky)
Animage Complete Collection