I saw Kikagaku Muyo at Le Guess Who? festival in Utrecht a couple of years ago and they were great!
As for me... the main one is B'z (probably the best selling band in Japan). I love them so much, but am sad that they don't allow their music outside of Japan the way other bands do making them a pain to collect (their last two blu-ray's set me back over £100!)
And I adore Boris (named as boris or BORIS depending on what type of album they do...everything from drone metal to J-pop). I love that the guitarist (Wata) does such terrifying noise, yet all her posts are about Pokémon or guitar pedals!
An example of regular BORIS
Drone boris (there are 3 versions of this song, but went for the live version as it is INSANE)
I also love weepy piano ballads. B'z do a lot of them, but as finding their music is such a pain, i'll go for this beautiful song by supercell
Finally - because no Japanese thread is complete with awesome anime music...