Microsoft states this happens because "...a file has the ".doc" file name extension, but the content is a plain text file or another kind of file that is not a Microsoft Word binary file, and that file is opened in Microsoft Word..."
This problem appears after installing Microsoft's security update 973904.
How to "fix" it:
1. Open the Registry Editor and browse to:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Shared Tools\Text Converters\Import\
2. Delete "MSWord6.wpc"
If you are not familiar with the Registry Editor:
1. Go to Start > Run... and type: notepad
2. Click OK.
3. Notepad will open. Copy and paste the following lines. Make sure you copy all three lines, meaning there should be a blank line in between the two lines with text.
Windows Registry Editor Version 5.00
[-HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Shared Tools\Text Converters\Import\MSWord6.wpc]
[-HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Shared Tools\Text Converters\Import\MSWord6.wpc]
4. Go to File > Save As... and save the file to your Desktop as: AllowImport.reg
5. Click Save. Locate the file "AllowImport" on your desktop and double-click it. Click Yes and OK and you should be able to open those files.
Update: Microsoft provided a "Fix it for me" solution for this issue.