For a great overview of music from around the world, and music for kids, I heartily recommend the Putumayo offerings.

Rembetika Players
Many countries have their own versions of the Blues, or current music that is a credit to their culture. Greece, where I spend a lot of time, has Rembetika, which was born out of forced migrations of Turks and Greeks based on religion back in 1922. Here is a great example of a Rembetis (a Rembetika player) Marcos Mamvakaris playing Φραγκοσυριανή . Don’t ask, my Greek is pretty basic. Rembetika songs are wistful, but often amusing, telling stories of wine (Retsina), women and hashish. It was banned several times by the authorities or occupying forces, but is now enjoying a resurgence. Φραγκοσυριανή is an example.

Huun Huur Tu
In the lands of the far east, there is a ton of music that we never get to here, for example Balinese and Javan. In Northern Asia, there is Tuvan folk music, and you have to listen to the music of Huun Huur Tu. Play around in their site too, listen to their music. It’s songs dedicated to the land and to their mothers. See if you can find them playing “Eki Attar”. Their web site shows an up-coming US tour so, if you can, go see them.