We needed a separate Word document for each record of the Mass Mailing and Word can not do that.
After searching for some time, I was ready to write a macro myself, but luckily I found Graham Mayor's website with a nice Add-in that solves the problem. The add-in will intercept the command to merge to a new document and provides an additional option to merge to separate document files:
Graham's website contains a ton of other Word Tips. I haven't checked them out yet, but it definitely looks worthwhile.