i am currently loving The Moor and Hessian Peel 
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I would also like to add Recoil to your list of Avant-Garde music...like nothing I've ever heard before, Alan Wilder at his best. <3Fourth Stage: The Madness: Zeuhl, Avant Garde, Mathcore, etc.
Frank Zappa
John Zorn
The Dillinger Escape Plan
Protest The Hero
Sleepytime Gorilla Museum
Magma
Univers Zero
Koenjihyakkei
Ruins
Bondage Fruit
Unexpect
Dün
Shub Niggurath
Mind you that this list is 100% subjective and is not complete.
Voxtrot, Someone Still Loves You Boris Yeltsin, LCD Soundsystem (get the album Sound of Silver), Cloud Cult (Get the album 'Advice From The Happy Hippopotamus', it's a masterpiece). If you like, check my last.fm for more ideas...I'm kind of obsessed with music.
you are missing some great Japanese bands, manJapanese Metal: Dir En Grey, High and Mighty Color
Sigh
Green Day <--- Not the new stuff unless you like pop-ish bands and not the very first album unless you like very fast angry things