The current titan of music streaming. A huge catalogue of music (30 million+ songs), with most genres and styles well represented. Spotify free allows you to find and stream music, and to create and share playlists. Ads are present in the free version, and offline listening is only available for premium accounts. On mobile, you cannot select specific songs. You choose a playlist, and can listen to it on shuffle and can skip up to six tracks per hour.
App available for Android, iOS, windows mobile and computer. Account required.