You can authorize five computers to play songs from the iTunes Store

As of 28 April 2004, you can authorize up to five computers to play songs bought with the same account from the iTunes Store.
Prior to 28 April 2004, the maximum number of authorized computers per account was three.

A note about copyright


iTunes software may be used to reproduce materials. It is licensed to you only for reproduction of non-copyrighted materials, materials in which you own the copyright, or materials you are authorized or legally permitted to reproduce. If you are uncertain about your right to copy any material, you should contact your legal advisor. See the iTunes Store Terms of Service for additional information.

Published Date: Feb 18, 2012