Windows to Linux Remote Desktop
I used to use nx for this - you'd want to install freenx from the repositories or the 'official' free version of the nomachine server and use the client from the nomachine site to connect to it
In addition to outperforming VNC, it'll start up a seperate, optionally persistant remote access session
Alternately you could find a windows X client (i'd suggest mobaxterm ) and connecting over xdmcp.
I'm aware of two ways you can do that:
Install a VNC server on the Linux box which functions as or launches its own X server rather than puppeting the one attached to the main display.
Install Cygwin/X or
Xming (thanks, jcrawfordor)VcXsrv and use X11's network-transparent design to run your remoted applications locally. It's a little less obvious how to do it, but it'll let you mix local Windows apps and remote Linux apps in the same desktop as if they were all local Windows apps.