[For Educational Purposes.]
Say you're playing some Pandora, and want the song that's currently playing for free...
-Firefox and the Firebug plugin
1) Launch Firefox and login to Pandora. Play your preferred radio station.
2) Click "Activate Firebug for this website" for mac users click the Firebug emblem in the window's lower right corner
3) Click the "Net" tab within the firebug pane. (enable it if it's not already)
4) Scroll to the bottom of the net tab. The item closest to the bottom that is larger than 1MB is the song currently playing.
5) Right click it and "copy location." Paste it into your url bar. Download it.
6) Rename the resulting download and change the extension to "mp3"
See screenshot below.