If you're using Word 2003 or earlier, press Ctrl+Alt+dash (top row between 0
and + sign). This turns the mouse pointer into a big dash. Click File, then
use that dash to click on the file you want to remove from the list of
recent documents.
According to the table of all keyboard shortcuts, that is "Customize
Remove Menu Shortcut." I defy anyone to explain what "customize remove
menu shortcut" means.
Its full name is ToolsCustomizeRemoveMenuShortcut. That's a throwback to the
days of WordBasic, when commands were named according to the menu/submenu on
which they lived; this one was in the Tools > Customize menu and has the
function of removing a menu item. I don't know why MS chose "Shortcut" rather
than "Item", but software engineers aren't necessarily good at consistency in
user interface design (cf. Alan Cooper's "The Inmates Are Running the
Asylum").