Microsoft was wise enough to not repeat the Word 95-Word 98 disaster. So you just copy those files to your new machine and you'll be able to open them (and update if necessary) in any later version of MS Word. No need for any conversion.
I use Windows XP and have been using Word 2002 for many years. It looks like I'll need to switch to Windows 8 pretty soon and will therefore also have to switch to a word processing program that is compatible with the new OS. I'm a professional translator and have loads of Word 2002 files that I'll need access to. Is it possible to transfer these files to current MS Word programs?