One of my personal favorite websites and applications of all time would have to be Grooveshark.
The Android application allows you to play virtually any song instantly to your device. Search and play an entire album or individual songs of your favorite musicians. If you have many songs that you would like to listen to, just create customized playlists either on your device or on the computer. There is even a radio feature to help you find similar music styles in the event that you run out of songs to think of. Add the songs to your offline folder and you can save the music to play when you do not have the best coverage. Grooveshark Mobile is free for Android devices but at this moment they are only allowing VIP members to use the service. A VIP membership costs either $3 USD a month or $30 USD a year.