SoundCloud
According to statistics published by the company in 2014, it is lifted 12 hours of audio on SoundCloud every minute! The application does not allow downloading of music files, but offers the possibility of unlimited broadcast millions of available tracks. Certainly will not find everything you're looking for here, but thanks to the huge library provides, there are always going to want to listen to him.
4Shared
Of the most famous and oldest share files on launch services, has a huge library of audio files searchable, which allows either direct to listen through the built-in music player, or download to your phone, or move the file and save it in your space within the personal cloud service. As with deciding BitTorrent BitTorrent, you can not describe 4Shared that piracy service even if it can be used for this purpose, and is available for many years legally through the Google Play store.
TuneIn Radio
While it is not an application to listen to music on demand, but the TuneIn gives you access to a huge range of radio stations around the world and listen to them directly, as you can not search for radio stations by language or country, but also according to music broadcast by type, and thus it is one of the best applications in this area.