This article is from the Anime Music FAQ, by Ru Igarashi with numerous contributions by others.
From Avatar's (a.k.a. Andy Kent) Japanese Animation Legality FAQ (http://member.newsguy.com/~memoirs/legal.html - note this is not being maintained at the moment, just archived),
No, you can't copy a CD full of anime songs either. @_@ Unless you're making a personal copy onto tape for use in your car or such, and even that's touchy from a legal perspective.
As some folks have pointed out, if you pay the copyright fee or whatever given stipulated terms, of course you can. Many music related clubs do this, and in some countries there is a levy on recordable CDs to accomodate the recording industry. Time shifting (e.g. making a temporary copy of a TV show while you are away from home so that you can see it when you get home), and space shifting (e.g. making a tape or MP3 of songs you paid for so you can listen to them in your CD-less car) have been allowed, but the allowances are quite restrictive. Copying MP3s from Napster, for example, when you don't own a legal copy of the CD they came from was ruled definitely illegal. One key issue of legality is that you have to own a legitimate copy (produced by rights holder, sold legally to you, or to an individual who then gave it to you) BEFORE you make any copies, or generate any other form of copy. If you can't prove that, you can assume your copy is illegal.
Otherwise, the Fair Use clause of any nation's copyright laws tend to be difficult to gauge, such that it is better to assume a copy is illegal. Keep in mind, that Fair Use clauses tend to be oriented more towards "purposes such as criticism, comment, news reporting, teaching, scholarship, or research" (US Code Title 17, Chapter 1, Section 107). At the very least, it's handled case-by-case.
 
Continue to: