This problem has actually happened to multiple clients of mine.
The issue is that the user will accidently try to open a Microsoft Word document with Adobe Reader. After that, it seems that Windows just does not know what to do with Word documents anymore, even after you tell it to open the documents with Word every time in the Open With dialog. (Although, now that I think of it, I did not confirm this to be true, I took the user's word for it. Something to check next time).
The thing that appears to have fixed the problem is to change the following value in the registry:
HKCR\.doc
Change the (default) value from word_auto_doc (or something like that) to Word.Document.8
Then right-click on a word document and select Open With, Select Program, select Microsoft Word, and check the Open with this program every time box.
Yet another annoyance with Vista / Office 2007. I will rant more about these in another blog, because there is soooo much to say...