Which version of MS Office is it? (2000, 2003, 2007, 20010) do you have the CDs to reinstall and the product key? (if no CD some are downloadable from MS to make your own, but you need to have your own product key in order to install)
Have you looked at the EULA.
In Office 2003 mine says I can have it on 2 pcs at same time so if I got rid of one pc and wanted to install it on another new one, I would have to unregister it on old pc with MS before I could activate/register on new pc.
Obviously if I was selling/junking old pc then I would unregister that copy to free up the license for new pc and not give a 'free' copy of office away.