I use the service to stream music that is completely paid for and legal. Allowing other users to stream the music I uploaded seems to be no different in principle than playing it on a loudspeaker in a public space. Do I have the right to let other people listen to my music? This doesn't seem to be a copyright issue because no media has been actually copied. Grooveshark allows multiple users to listen to a single, legally owned copy. Grooveshark not only removes copyrighted material upon request, but also blocks uploading privileges for users who have violated the rules.
It is also not the case that they are acting selfishly and without regard for the industry. They are constantly taking steps to work with the major labels and have already closed a deal with EMI. Only Universal is suing them. They also have a profit sharing program with artists and do seem to care about finding new revenue streams for the music industry.