The only Japanese band I know is Mono.

If you like instrumental post-rock music in the style of Mogwai, Explosions in the Sky and Godspeed You! Black Emperor, you would do well to check out Mono.

Oh well, I have some favorites...
Amano Tsuki(ko)
Utada Hikaru
ANZA/Head Phones President
Rider Chips (duh!)
Tanimoto Takayoshi
Ito Yuna
Yumemiru Adolescence
JAM Project

But I generally listen to whatever I feel like, sometimes AKB48, sometimes Hamasaki Ayumi, maybe even Amuro Namie...