Although my gut feeling is that there is something wrong with recording a song off the radio, I can't come up with a reason why it would be different than using a VCR to record a movie off TV.

Recording a song off the radio or a TV program with a VCR are specifically protected-by-law. And the record companies and TV/Movie companies don't mind when you do it because all that stuff is still in the analog domain and any copies are obviously inferior to the original. No one ever makes money selling copies of songs taped off of the radio. The record companies are not worried about this happening because it doesn't take away any of their business.

The only reason they're upset about MP3 and DVD piracy is that copying a computer file results in no generational loss. Hence the possibility for large scale redistribution without the "inferior quality" part. That's the difference, and that's where the line is drawn. Or at least, that's where they're trying to draw it.