Yes, but it'll cost you. The two services are PressPlay, backed by Universal Music and Sony Music Entertainment, and MusicNet, backed by Real Networks, Warner Music Group, BMG, EMI Recorded Music, and Zomba Music. Both MusicNet and PressPlay are essentially Napster copycats allowing users to find, organize, and share music for a monthly fee. However MusicNet will distribute its music packages to corporations like AOL and Napster, who will in turn charge the consumer their price for access.
None of these 'solutions', however, address the issue of just burning a CD from the found MP3s. There's really nothing stopping anyone from trading music, and burning CDs; if it comes out of your speakers, it can be burned and copied.
Remember those plastic cartridges about 12 years back? I think they were called cassette tapes. I also think I had about 500 tape mixes that I made by 'borrowing' the original tape from friends and recording onto brand new tapes. Then these tapes could be traded or sold to friends or through mailing lists, or through the various News servers and BBSs around the world. I don't remember anyone making a fuss over that. Or was I just asleep?