The ultimate classical avant garde composer is definitely John Cage. His arguably most famous piece is 4'33". It is comprised of three movements, during which the performer plays exactly ZERO notes. Yup. It's complete silence. It's named 4'33" because that's how long the premier performance of the piece took. He has also done radical compositions using electronics as well as more standard fare including the wonderful Concerto for Prepared Piano and Orchestra (a prepared piano has various items stuck inside of it to achieve a desired percussion effect or warping of the standard piano sound). He even once wrote a piece for 12 radios to be tuned to certain stations at different points in the composition.

Almost all of his music is aleatoric, which means certain aspects of the performance are ambiguous, and each performance will be completely unique and different. He is also known for creating some truly unique and obscure looking scores. Check out some of these:

http://www.kunst.uni-stuttgart.de/wendland/progetti/mondovi/fontana.gif
http://eamusic.dartmouth.edu/~music3/images/cage-williamsmix.jpg
http://growabrain.typepad.com/photos/uncategorized/john_cage_score.gif
http://rafaeltoral.net/pictures/04_rafael/scores/sf2psmap.jpg
http://scorecard.typepad.com/photos/uncategorized/score_for_sound_111305.jpg
http://homepage1.nifty.com/iberia/cage_australes29-1.gif
http://deposit.ddb.de/ep/netpub/97/03/78/957780397/_data_dyna/_snap_stand_2003_03_27/2003/2003_2/2003_2g1.jpg

Pretty crazy huh?