Well, you asked for suggestions from the UK. The British folk revival was fuelled by the skifflers interest in American folk songs. and apart from that there has been a wide knowledge and appreciation of American folksong over here for generations.
    I'll pick out three that seem (from this side of the pond) to sum up America's musical greatness in one way or another. And I'll stick to traditional folksongs, not modern known-composer stuff.
You've got to recogise the overpowering contribution of black culture to American music, so I suggest Leadbelly's version of the Midnight Special as a fine example.
    The main thing we all know of American history is the extraordinary physical feats of those early explorers and traders (yes, and exploiters) who opened up the country. A song that seems to me to have the perfect feel for the vast open spaces they encountered is Shenandoah.
   For the white culture, what could you pick out? I think Jesse James might fill the bill. I appreciate that historically the man was probably some squalid racist hoodlum and who knows what besides, but the song has enabled him to achieve some kind of apotheosis. And lets face it, guns and horses and train robberies and stuff is pretty much what we all think of America anyway.
So that's my choice. All fabulous songs, and in particular a delight to sing along with.