My daughter (also six) likes Phil Wickham, Chris August, and I really love Jeremy Camp myself. Those are all Christian artists.
They Might Be Giants are my favorite band, and my daughter loves it. They're fun, quirky...they do make a few children's albums, but we listen to the real albums.
We also like to listen to Schoolhouse Rock together....lots of fun, sounds like adult music, but educational.
What else? Bob Marley, Keane, Charlie Brown album, Swing Kids soundtrack, Gordon Lightfoot, Don Williams, the Beatles, Raffi...
Oh, and the best are probably oldies. We listen to lots of music from the 50s, 60s, and 70s...the classic 50s rock (she loves Poison Ivy, Willie and the Hand Jive, Personality, Poetry in Motion...those are just examples)...from the 60s, we listen to things like Green Tambourine, Grazing in the Grass, etc...and 70s pop as well, like Paul Simon, earlier Elton John, etc. Love it all. :)
Oh, someone else also mentioned the Nutcracker...don't discount classical music!! My daughter has LOVED the Nutcracker and Swan Lake for years, as well as a ton of other classical music. She listens to NPR! :) I also agree that Peter and the Wolf is great (I've been a fan since I was young) and you know what else totally rocks?
The soundtrack from Wall-E. It's become a favorite of mine....BEAUTIFUL music, mostly instrumental, but a few with lyrics.