I just learned about the existence of Xnest. It’s probably not as nice a solution as using the commercial nx software (or whatever advantage of VNC is) … which we presume has lots of clever stuff hidden inside… but it has the advantage of not needing any additional service to be run on the remote machine, and Xnest already being in the debian repositories with all convenience and open sourceness that entails. Log in to shell on remote machine using ssh, then start this Xnest program.
Xnest can be used locally, for example to allow creation of a parallel nested xsession with different window manager. Just like other gui applications it can be started if you are log in using ssh and allow xforwarding (using x11 on unix or available with for example cygwin on windows). This allows you to log in remotely and start gnome session in a window, giving remote desktop.
Xnest -geometry 1150x750 :1 &
xterm -display :1
Then start for example gnome-session from the xterm embedded in the Xnest window.