No (assuming you're not talking about old beta versions, in which case it
would depend). In fact, if you're installing an upgrade version of Office,
you'll need to have the old versions present in order for the upgrade to
work. Office's setup program will remove the old version when it installs
the new (and, except for Outlook, I believe), you will have the option to
keep the older program, as well. (I kept Word 2002 installed when I
installed Word 2003, because I need it for a Word 2002 tutorial/tips
newsletter I write).