Is there any way to force Visual Studio to copy selected code to the clipboard as unformatted text?
When I am copy-pasting code into Word or more often Outlook
This Microsoft Office site offers a workaround that involves writing a macro to replace ctrl+v functionality to paste plain text all the time, but that may not be what you want. You can alternatively remap an unused shortcut (ctrl+?) to provide you with this functionality so you don't have to keep enabling / disabling the macro.
You might find http://www.extrabit.com/plaintextclipboard/ to be a useful tool. Some applications have a paste option which strips formatting, but what you really need is a copy operation that strips formatting, which VS does not offer.
Visual Studio does put unformatted text on the clipboard, but it also puts formatted text. (The clipboard supports multiple simultaneous formats, and the OS assumes that they're simply different representations of the same data, although there's no technical enforcement of that point.)
The application you're using to paste then chooses its preferred format. In Word, and maybe Outlook as well, there is a "Paste Special" command that allows you to choose which format you want to use.