There is a Czech trad-jazz group who regularly busk (or did) on the Charles Bridge in Prague. Their instrumentals are pretty good but the result when they break into Basin Street Blues in a heavy Czech accent takes it to a whole new level. This must be going on all over Czechoslovakia with bluegrass.

There is a genre of songs that are intended for singers with foreign accents. One we've tried with our Middle Eastern band is Ya Mustafa, which was was originally written in Arabic by an Egyptian composer for a Greek-Egyptian whose accent was famously weird. It went on to be an international hit in a tossed salad of different languages. We're using at least Arabic, Greek, French and Italian, with none if them sung exclusively by native speakers. I've volunteered to contribute some of the Catalan version if needed (I only know a few words of it).