I like some music from Japan, though most of the anime themes I've heard make me cringe.
I'm currently being rocked by these:
Aoki Takamasa (Ambient, Glitch, Minimal Techno)
Buffalo Daughter (Clever mix of Lo-Fi Rock with wobbly vintage synths)
Coaltar of the Deepers (Shoegaze Rock with some forays into Thrash Metal)
Cornelius (Early stuff goes from Big Band / Lounge to the textured ambience of later work)
Denki Grove (Tongue-in-cheek Techno, inspired by YMO and Kraftwerk)
Hi-Posi (Utterly bizzarre Electronic stuff that I need to listen to more to formulate a better description)
Kahimi Karie (Whispery loungepop with English, French and Japanese lyrics)
Mayumi Kojima (Big Band, Blues, occasional wonky Baroque)
OOIOO (Lo-Fi / Psychedelic Rock)
Polysics (High-energy punk, influenced by Devo)
School Food Punishment (Power-pop - they have a lady singing over pianos!)
Tujiko Noriko (COLD, FRAGILE MISERY.)
Also, A few of the above have contributed tracks to anime openings / endings.
WHERE IS MY KORORINPA 3