This was an exciting discovery for me.  While using the Last.fm application on your computer, and listening to the "Neighborhood" station, you can click on the "Playlist" button to add the currently playing song to a personal playlist. 

Once the playlist is long enough, you can play it from your personal profile in the last.fm website (click on the "Play in software" link) and enjoy listening to full versions of only the songs you selected.  You can't control the order, but it's all the music that you like, exclusively, and commercial-free.  Nice.