I'd say the most influential music of the 20th Century was the Beatles. Or the most noteworthy. Or the most popular. Or something. Basically, it's the band with the biggest name recognition and basically everyone likes at least some of their stuff.
What would be second runner-up? And is there anything of this age (3 decades later) that even compares?
I threw out a few names like Nirvana, Radiohead, Aphex Twin, and Lily said Green Day or ACDC... but none of them were or have been around for as long as the Beatles, nor do I really see them being recognized as so important in, say, 30 years.
We were also talking about how in an MTV era, it's almost impossible to gauge something like influential music. Throw charts, MTV, radio, whatever into the equation and you've got skewed results from the majority of people (read: SHEEP) who will listen to what's popular. This isn't to say that the Beatles' popularity wasn't skewed by stuff like this... but back then when music was under less attack by corporations and IP debate, it was quite a lot harder to become an "overnight sensation," or something like that.