I typically want to use VNC to connect to an existing X session. x11vnc does the trick. This page helped me figure this out.
apt-get install x11vnc
On a trusted network, it is safe to:
far-away> x11vnc -display :0
sitting-here> vncviewer far-away:0
Otherwise you’ll want to tunnel VNC over SSH:
sitting-here> ssh -t -L 5900:localhost:5900 far-away.east 'x11vnc -localhost -display :0'
sitting-here> vncviewer localhost:0