I've been needing to be able to remote desktop my new Ubuntu machine from the login screen and information on the net is always confusion. So here I will share my solution I ended up with. This is how you access your machine over VNC from the login screen with Ubuntu 13.10 which uses LightDM for the display manager.

Install x11vnc:

apt-get install x11vnc

Then create /etc/init/x11vnc.conf file with the contents as below (ending at end script):

start on login-session-start
script
x11vnc -xkb -noxrecord -noxfixes -noxdamage -display :0 -auth /var/run/lightdm/root/:0 -rfbauth /etc/x11vnc.pass -forever -bg -o /var/log/x11vnc.log
end script

Run this in terminal replacing PASSWORD with the password you want. Use a space at the beginning to not record in bash history.

sudo x11vnc -storepasswd PASSWORD /etc/x11vnc.pass