I found the following web page thought-provoking: http://www.bargaineering.com/articles/buying-vs-streaming-music.html
This is an interesting analysis, but is a false dichotomy (i.e. that you have to pay to stream vs. pay to buy a song). There are other options, as mentioned by a few people in the comments. For example, Pandora, Grooveshark, Spotify, and Last.fm are well-known free music streaming services. Lesser-known ones are listed on Lifehacker, along with strengths of each: http://lifehacker.com/the-best-streaming-music-services-you-arent-using-but-476372723
YouTube is also an overlooked option: it offers auto-playlists based on certain songs or bands that you like, or you can create your own playlists and add songs to them. You'll have to put up with ads on some of the videos, but it does allow customization and a high degree of user control--all for free!