That song is called "Flightless Bird" by Iron and Wine. It is currently my favorite song.
I love it.
Anyway...Heres what I think for the Cullens:
Carlisle & Esme-I think that they would both listen to "oldies."
Emmett-rap and rock. Like Meztli said, I can see him cruising down the street in his big ole jeep acting cool.
Rosalie-this one is a bit harder. I think she might like hip hop.
Alice-I can see her listening to everything. She probably likes the kind of music Edward listens to the most, though.