F11 makes a window go full screen. Is there a shortcut that minimizes a window? I am using Arch Linux with Gnome Shell.
Gnome Shell actually supports this. Super+H is the default key. If you want to change the key go to:
Settings -> Keyboard -> Windows -> Hide Window
On the GNOME desktop environment, you can use CTRL-ALT-D to minimise all and give focus to the desktop. You can also use ALT-F9 to minimise the current window. I think these are the same for Ubuntu/Unity.