Reader Paul writes in with a useful tip: You can use the previously mentioned FileTypesMan utility to hide certain file types from showing up in the Recent Documents folder.
Once you've opened up the no-install-required application, just browse down until you find the file extension you want to hide, double-click on it, and then check the box for "Don't add this file type to Recent Documents". It won't clear out anything that's already showing up in the recent documents folder, but they shouldn't show up in the future.
Of course, that's not the only thing this excellent Nirsoft utility can do—other than being an excellent replacement for the built-in Windows file types tool, you can also choose to always show the file extension, add it to the New menu, or disable the confirmation when downloading that type of file. Thanks, Paul!