You don't have to register Office, but you do have to activate Office XP
or Office 2003.
Read your End User License Agreement to see what terms apply to your
copy of Office. Generally speaking, an OEM copy of Office cannot be
installed on any other computer than the one it came with, and a retail
copy of Office can be installed on one desktop and one laptop owned by
you. But there are exceptions... as examples, Office XP for Students
and Teachers can only be installed on one computer, Office 2003 Students
and Teachers Edition can be installed on up to three computers, and some
promotional copies of Office can only be installed on one computer.