As someone stated earlier, the problem with a definining artist for this generation is the way this generation lives it's life. This is the generation that has grown up on the internet, IM, blogs and a steady diet of fast-paced, ever-changing interests and trends/fads. They've been programmed to love something and then discard it and move on to the next. Depending on point of view, does this generation have ADD or does it excel at "multi-tasking".
Being a Gen-Xer, I was deemed as being lazy, a slacker, having general apathy and no real goals in life. However, today, Gen-Xers are looked at as innovative, risk-taking and unconventional. I'm convinced that my generation was defined by some great artists who produced some of the greatest albums of all time. These albums captured a distinct snapshot of society at that time. While some "good" albums have been released in the past 10 years, none have been what many would call "landmark" or "must have". No White Album, no Zeppelin IV, no Dark Side of the Moon, no Joshua Tree, no Nevermind.
Artists do not define generations anymore, music executives do.