My knowledge of Japanese music is somewhat limited, but I do have a few favorites.

J-Rock, thanks to FLCL, I have taken a liking to The Pillows. (I now have both the FLCL OSTs.) And there's a band called Mr. Children that I like just for the name, though I've heard a couple of songs by them. :lol

And more on the J-Pop side, I got into Puffy before any of their cds were even released here, and before they hit the relative big time here with the Teen Titans theme. (and before they were forced into adding the "AmiYumi" to their name) I got "Spike" soon after it was released here. I'm glad I was ahead of the curve for them. :)