In OS X El Capitan you can screenshot the login screen using the standard full-screen shortcut (Shift+Cmd+3) or the drag-to-select keyboard shortcut (Shift+Cmd+4). In earlier releases of OS X it’s always been borderline impossible to do this.
The image is then saved to the desktop of the next user who logs-in. Notably, this doesn’t work if you have FileVault enabled, unless you manually log out via the Apple menu to return to the basic login screen.
(Via Der Flounder.)