Yes but for free, on mobile you can just pick a song to listen to - you can only listen to playlists, artists & albums in shuffle mode. I think it is a great service & my favorite since MOG got eaten, but I prefer the paid service so I can download songs & listen off line anytime, plus the audio quality is much, much better.
Spotify music is great because it is free, you can install the Spotify app on your mobile device and listen to spotify freely. However, one thing you can't ignore is that Spotify music are DRM protected, so you can't directly download and transfer the OGG Vorbis Spotify songs to MP3 players for playback. But don't worry, after searching online, I does fine some tips on how to download spotify songs Take a look at it if you like. By the way, after downloading, you don't need the premium membership anymore. So you will end up using all the spotify songs for free.