If you have Office XP or later - the installation uses and activation scheme that ensure that Office is installed on the number of machines specified by the license.
That being said, If you purchased a retail version of Office XP, the end user license agreement (EULA) permits installation on a desktop computer and a laptop computer.
If you were to have Office installed on a “older” PC, and then you purchased a new PC. You could delete Office off of the old PC and call Microsoft (once installed on the new machine you will be prompted to call Microsoft once it recognizes/thinks the license is already inuse). Microsoft will ask if you’ve deleted Office off the old PC and then give you a key to install it on the new machine - all based on an honor system since Microsoft can’t tell if you really delted Office off the old PC.
Good luck,
-C-