Originally Posted by cardboard adolescent

Avant-garde is usually associated with modernism since a large part of that movement was "pushing boundaries." Thus, most minimalist, drone and early electronic music was considered avant-garde.

Edgar Varese is very important since he basically invented musique concrete and is considered the father of electronic music. Karlheinz Stockhausen did a lot of experimentation with electronic music as well, as well as chance-based compositions. Along those lines, John Cage is a very important avant-garde innovator as well, especially for his incorporation of Eastern philosophy into music theory. You have Stravinsky, I would mention Schoenberg as well for rejecting traditional tonality. Then there's the minimalist boys like Phillip Glass, Steve Reich, and Terry Riley. Post-minimalism includes artists like Glenn Branca. La Monte Young is probably the most important early composer for drone music, though many of the artists which champion it today are rock bands.

As far as free jazz goes, Ornette Coleman, Cecil Taylor, Albert Ayler and Sun Ra are some very important players. From Europe you have Peter Brotzmann who pretty much blasted his way through all sax-playing conventions.

John Zorn kind of keeps free jazz alive nowadays though often with very heavy rock and thrash influences, so bands like Naked City are pretty important as well. There's a lot of free improv music that doesn't easily classify into jazz or rock, some of which is fusion and some of which is simply neither. AMM are a very important early free improv band, and groups like A.D.D. Trio show off the more fusion side to it.

As far as avant-rock goes, the most obvious originator is Captain Beefheart, who basically threw free jazz and rock together for the first time on Trout Mask Replica and changed music. Then you've got stuff like The Residents who metamorphosed rock with their dada leanings; Velvet Underground, Sonic Youth, JAMC, etc. are all seen as very important regarding introducing noise as a viable stylistic element into rock music, with artists like Merzbow, Whitehouse, Nurse With Wound, and Throbbing Gristle taking that concept to its logical extreme (that is, they are noise artists).

On the drone side, you've got stuff like Sunn O))), Earth, and Boris giving minimalism that metal aesthetic.

You've got a ****load of other artists to work with as well, such as Fred Frith who does everything from noise to avant-pop, Jandek who is one of the more popular "outsider art" musicians, or John Fahey who brings avant-garde to folk music.

I don't know too much avant-garde metal, but Ulver gets namedropped a lot.

these are the genres I'd consider:

avant-rock (I would consider RIO a subgenre of this)
musique concrete
free improv
free jazz
noise / power electronics
electroacoustics
minimalism / post-minimalism
drone