How to quit without saving using just the keyboard? When I quit an application (e.g., Excel) with Command-Q, a dialog box pops up, asking me to select between don't save, cancel and save.
I can hit Enter to select save, or I can navigate the mouse to don't save, but how do I get that without the mouse?

On Linux and Windows I can use Tab to switch between the 3 buttons.

What do I do on Mac OS X? 

Excel for Mac 2011 (14.3.8)

I tried: 


Tab
shift-Tab
control-Tab
option-Tab


No go.
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.