From Mark Harris,
Your Guide to Digital Music.
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A.

Under US copyright law, if you convert (rip)an original CD that you own to digital files, then this qualifies as 'Fair Use'. As long as you use it for your own personal use and don't distribute the copyrighted material to others, then you will not be breaking the law.

According to the RIAA web site, it's acceptable to make a copy of an original CD as digital music files or to burn one copy for yourself, but not to share with others.