Bonnie Pink - her Even So album is possibly the most relaxing set of tracks i've ever listened to.
Shiina Ringo - Shiina is definitely the First Lady, as you may, of Japanese Rock, and a fountain of talent to go with it. (may also want to try Tokyo Jihen, the band she fronts).
X-Japan - need i say anything? Basically starting the Visual Kei genre, this is the rock band that i compare every other rock band in existence to, be they asian, American or European.
Dragon Ash - The group that made rap tollerable to me.
L'arc en Ciel - Still going strong, one of the most popular bands in japanese history. I remember reading that along with X-Japan and Luna Sea, L'arc success prompted the quality of Japanese CD's to rise dramatically.
and if you're feeling a bit adventurous (80's - early 90's)...
Akina Nakamori - the 80's jpop diva, excellent voice and great music (from the sadly limited amount i've heard).
Noriko Sakai - the Jpop star who first captivated my heart. Her voice is simply amazing, her music captivating and she can even make 80's fashion look awesome.
Miyuki Nakajima - Not 100% 80's here, considering she began her career at the end of the 70's, and is still going today. a captivating voice and excellent tracks, ranging from soft to powerful and even sometimes a little obscure/unique, there's something to please almost anybody with Nakajima's music.
Well, there's some that i recommend, hope it helps
