One of my favorites was Radio Barquisimeto, which used to be on the 60 meter band out of Venezuela. Supposedly they are online now, but I haven't tried to catch their stream yet. They always played cool music.
Another favorite was the old Radio Moscow. Propaganda? yes, but it wasn't 100% propaganda, as the cultural programs were usually quite interesting, including a lot of the cool music coming from Central Asian republics.
Another was VOA -- the old VOA, which had the jazz show and the Breakfast Show in English to Africa and Asia.
The Australian ABC outlets on 31 meters were cool to listen to (VLW9 was the one I listened to -- a SW relay of 6WF/6WN in Perth), as they were SW transmitters relaying ABC MW radio stations.
Papua New Guinea was a regular here on the West Coast, as was the Solomon Islands SW station. I think both are gone.
Last but not least, the Singapore Mediacorp SW stations were always cool. One was in English and the other one (I think it was called Radio Oli) was mostly in one of the Tamil-related languages (from Southern India). I used to hear them most mornings, along with the RT Malaysia SW station out of Kuching, Sarawak.
I also remember Radio Nederland and HCJB, but didn't listen to them as much as I did Radio Australia and the stations coming out of the Pacific.
Someone here mentioned Afrique Numer Un -- I remember hearing that one on 31 meters during the late afternoons. Lots of soukous and highlife music, it was always very cool to hear.
Of course, nowadays we have internet streaming, but it's not the same. On one hand, the streams are FM quality. On the other hand, internet connections to some areas of the world are still a bit dodgy. I've tried getting Iranian stations using Tune-In -- sometimes you get streaming, sometimes nothing. And other stations -- like the Voice of Greece, for example -- apparently don't have streams. The Voice of Turkey used to have a musical program aimed at Europe that I could hear for six to eight hours on my DX-390 and maybe 40-50 ft. of wire. Now I'm lucky if they're running their internet music stream more than a couple hours a day. Most times I check it it's turned off.
Welcome to the new world of international radio.....