Remote Desktop for Ubuntu

"Take a look at: http://www.nomachine.com/

NoMachine NX is awesome because it gives you a remote desktop over ssh so it is a secure connection. You install the host on the machine you want to remote into and the client on the computer you want to use to control the other computer. They have versions of NX for Mac, Linux, and Windows, so you can remote from any O/S into any other O/S. It is really great free software, it will amaze you how well it works."

"I definitely am not going to win the bounty for this but, here goes...

What you want to do is called X11 forwarding over SSH. You can run an actual Xserver on your windows machine using Cygwin and have it work with the Linux box over ssh.

It is a pain to set-up even without wrestling with firewalls and port forwarding. But, if you can ssh to the Linux machine from your laptop, you should be able to do it."