In the MOSS sites that have annonymous access and anonymous users, opening of an office document in a document library always requires entering username and password. If you cancel the prompt, the document still opens, but the prompt is annonying.
To prevent this prompt, change the linking to the document. That is, hyperlink to /sub1/Docs/mydocument.doc (where sub1 is the subsite, and Docs is the document library), should be changed as following:
Changing hyperlink to the reference would result into a simple download prompt of the document.
For more reference, visit the following post: