Is recording music (using Sound Recorder or some such tool) played from
the Computer legal?  I am not talking about ripping files off a CD or
copying a file from some one else.  Rather playing music from a radio site
or other music site on the PC and recording it into an mp3 file.

Hi Krishnakumar_kumar

In the US it is not illegal provided certain conditions are met by the
Audio Home Recording Act (AHRA) 1992.

"No action may be brought under this title alleging infringement of
copyright based [...] on the noncommercial use by a consumer of such a
device or medium for making digital musical recordings or analog
musical recordings."
http://www.copyright.gov/title17/92chap10.html#1008

The definition of noncommercial use was tightened by the No Electronic
Theft Act (NET Act) 1997.

for further details see
http://en.wikipedia.org/wiki/Audio_Home_Recording_Act