Aidee: it's a complete reinstall. You'll need to reinstall Office, then copy across all your Word, Excel etc. files. If I understand correctly, it's all about the registry. Your new machine has a registry that is unique to it. It holds details of where programs are installed etc. If you just copied back your application files from your other computer, the registry wouldn't know where to find them, as it's updated by the installation process. The same applies for all programs that you install (as opposed to e.g. run self-contained from an .exe file).

Others may know more/better.

Happyhacker: you're right, they're generally single machine licences. However, what that means is "just one machine at a time". If you uninstall a program from one machine, or scrap the machine that it's on, it's perfectly legal to install the software on another machine. In fact, in the case of older software like Office 2003, it's a moot point anyway, as that uses just a simple key which, so far as I know, is never validated by Microsoft online anyway (I may be wrong). With newer software that requires validation, it may be necessary to contact MS to revalidate it, and they'll want to be assured that the license is only being used on one machine.