Poddradio is the application from SR Världen (Swedish Radio World) which broadcasts one of the most consistently varied mix of world music. At this point, the only application where you can see the titles of the songs played.
VisuaRadio (does not respond to e-mails) and FStream are two French pieces of software with a wide-range of stations available. VisuaRadio has a beautiful interface but the names of the songs does not appear. FStream is better on that level. Just a few of my favorite stations: the inimitable LibraRadio, RadioDzair-Sahara.
Tuner and 00Tunes probably have some potential but I have not explored them enough.
Pandora and Last.fm have similar ways of collecting your musical likes and dislikes, and thus on providing you with a more and more accurate version of your musical taste. Choose as many “stations” as the number of types of music you enjoy, but be forewarned that some of their world collections are limited and you might see lots of similar albums repeated.
The are two Public Radio applications, one on this page. NPR News is the other. They have each their own advantages.
RadioShift, FlyCast, ShoutCast, and Stitcher I have not used yet much, although ShoutCast has access to the thousands of ShoutCast streams.
Deezer is a good way to explore French variety, but you cannot forward or customize the variety of French music heard on it. Some of the channels include French Rap, Chanson Française, Nouvelle Scène.
RadioFrance is a simple way to have access to France Culture, France Musique and France Inter, as well as many podcastst from some of these French networks.
France 24 is a way to get (preferably through wi-fi) to watch a live feed of the TV network France 24, either in French, English or Arabic.