A Raggedy Edge show is a study in diversity. Their song list includes many genres, from blues to country, pop to standards, rock to bluegrass, alternative electronica to completely unplugged and natural.
Besides originals, the duo's favorite music tends to default to traditional pop, aka American Standards. You can read more about them on their Littlest Big Band
And of course, they pepper their lists with covers from the current century, as well as classics from the 1960s through 1990s.