Via runme.org, Jon Meyer has a browser-based performance of John Cage's 4' 33". I found my attention turned to the motion out the window rather than any ambient sounds.
One more question: is this stuff really classical music? I think so. The huge variety of music of all eras that we call classical (and here I'm certainly including classic pop, folk, blues and jazz) seems to share two key traits. The first is a respect for tradition. Beyond being a wickedly keen variation on the conventions of the formal concert, 4'33" fills a crucial slot in history. Music began as an imitation of natural sounds and human voices but then became increasingly stylized. Cage brilliantly brings the process full circle, bridging the cultural distance that has developed between conventional performance and the sounds of nature where it all began.
The second hallmark is staying power. I've heard Mozart's dozen mature piano concertos dozens of times each over dozens of years, but right now I can recall only a few of their melodies. I heard the Cage piece just once (and three decades ago), but I remember it so vividly.
Guttman goes on to highlight Lucier's I Am Sitting in a Room and Reich's It's Gonna Rain as other successful examples of contemporary music. And yes, I can get tired of a work through too much repetition but unlike say a film or a book, I think music, due its brevity and abstraction, holds up well to thorough replay.