Once existing supplies run dry, 2003 will disappear altogether from shelves and new PCs. As with most Microsoft products, companies or people wishing to use 2003 on a newer machine will be able to via the “downgrade rights” option on a retail license for Office 2007. As the article mentions, however, the same option is not available for OEM versions, which makes sense as OEM must be bundled with a machine.
Indeed, running Microsoft software is a privilege, not a right! That being said, ultimately it is always a good idea to keep systems up to date, particularly when Office exploits are so common. I wouldn't expect them to stop support for several years to come, and security updates for even longer, though.