How to quit without saving using just the keyboard?
The standard shortcut for "Don't Save" in the dialog you mention is command ⌘+Delete. The old shortcut, command ⌘+D, can be restored by issuing the following command in Terminal:

defaults write NSGlobalDomain NSSavePanelStandardDesktopShortcutOnly -bool YES

and to revert back, 

defaults write NSGlobalDomain NSSavePanelStandardDesktopShortcutOnly -bool NO

In Microsoft Office 2011 for Mac, command ⌘+D seems to work by default (but the standard shortcut does not).

Basically, try either command ⌘+Delete for Apple or standard applications, and command ⌘+D if that does not work.