Linux GUI application running on server, seeing its output on Windows client: Solution is simpler than the problem. Following are step-by-step instructions to do it using Xming and Putty,
Download and Install XMing on your windows machine.
Download link: http://sourceforge.net/projects/xming/
Complete installation after downloading, do not yet run anything.
Download Putty for your Windows flavor (No installation is required, downloaded file is executable itself)
Launch XMing (from desktop icon). No window will appear, it should now be silently visible in your system tray.
Launch Putty. Putty’s configuration window will appear.
In configuration window, select “Connection->SSH->X11″ and set “Enable X11 forwarding” check box.
Click on session again, give the server name. (Linux server address/hostname on which application will actually run).
Putty terminal will appear. Log in specifying username and password. From prompt, launch your GUI application specifying command. For example, I have launched xterm in my session.
Xming will open a new window for the GUI on your windows machine. The graphical output of the window will appear within Xming window.