Music Download Center is a free app to download music and listen to radio. The app lets you browse a very extensive list of Internet radio stations, and it also lets you search for songs directly. The radio stations are sorted into genres and year. There are 90s and 80s radio stations, and lots of Pop, Rock, Reggae, etc.
When you first launch the application, you will see a pop-up window telling you that download music is illegal in many countries, and if it is in yours, that you shouldn't do it and you should only use the application to listen to Internet radio stations.
To download a song, you simply search for it and click on "Download", and an MP3 file will be saved on your computer. There won't be any DRM protection applied to this downloaded file, so you can play it on any device.
In my testing, both downloading music and listening to radio stations worked like a charm. I tested maybe 10 different stations and they all connected fine and started playing instantly. The quality of both the radio stations and the downloaded files was great.