Radiohead were one of the first major artists to do a 'pay what you want' which included $0. I believe they regretted it and I think I read one of the reasons was that it devalued music for everyone. e.g. if they are giving it away why do others think they can charge?

A few years ago, Reznor tried a kind of shareware-style "first episode is free, buy the full version" model with the Ghosts 4-disc set: Ghosts I was free, but you had to pay if you wanted Ghosts I-IV. You could buy either physical version of various levels of fanciness, or DRM-free downloads (MP3 or FLAC).