This makes me wonder a couple of things:

Will Apple, Microsoft and the MP3 player makers will fight this?

How would the RIAA find out who has ripped CD's to their PC, unless they propose some sneaky invasion of privacy method?

They really can't unless they have some kinda of monitoring software on your computer. This is something Sony tried to do, but claimed they were "unaware" that one of their firms did this. They also later stated that people shouldn't care what they install on their computer if they don't understand what it does.

Pretty f&*&ng stupid.

Anyways, I don't believe that it should be illegal to make legitimate copies of your own music as a backup or whatever. To do anything besides that is obviously wrong.

Also, did they just claim that it was "illegal" because they don't agree with it, or is it actually illegal?

From what I understand, it is perfectly legal to make backups for your own personal use. But backing something up, then copying it to another disk and either selling it to someone or even giving it away is considered illegal.