I don't know many japanese bands (that list looks worthy of checking out
but my favourite that I've heard is The Pillows, just checked their wiki page and noticed that they have done work with anime:-
The Pillows - Wikipedia, the free encyclopedia
Out of about 6 albums of theirs that I've heard the one that is the most inviting is 'Happy Bivouac (1999)', check it out!
Another good japanese band that hasn't been mentioned yet is Thee Michelle Gun Elephant, they broke up in 2003 but released alot of good material mostly around 2000.