Songza is pretty great for this.
iOS: https://itunes.apple.com/us/app/songza/id453111583?mt=8
iOS app is US only and the website is broken. When I click on the play button it redirects to the home page.
Working or me right now in Chrome...
Check out http://molli.es! I made this only for EDM music right now, but ya I just wanted the very basic site that plays music, and trying to bring back visualisations. Miss those from the Winamp days!
Recently came across Noon Pacific that does exactly this. Loving the service:
http://noonpacific.com/
Also, I'd like to be able to play it while I'm on a train. Pre-fech 30min of music to play when I'm underground and I have no internet connection.
If there is a hacker (London-based ideally) that want to work on that idea give me a shout on lukasz.madon at gmail.
https://developer.spotify.com/technologies/spotify-ios-sdk/