The answer depends on whether you have an OEM or retail copy of
Office 2003 Professional. Generally, an OEM copy (one that came
preinstalled on your computer by the computer manufacturer) is
only licensed for installation on the computer that the computer
manufacturer put the software on, and a retail copy (one that you
purchased separately from the computer and installed yourself)
may be installed on one desktop computer and one laptop computer
owned by you as long as you don't use both copies of Office at
the same time. You can read the End User License Agreement that
applies to your copy of Office by starting Word and clicking on
Help | Microsoft Word Help | Contents | <expand the "Microsoft
Word Help" category> | End User License Agreement. The "Grant of
License" section in the EULA tells you how many computers that
your particular copy of Office 2003 can be installed on.