Okay, X Windows is the usual GUI involved in most Unices, including Linux. X Windows is networkable, by which I mean that the UI need not be displayed on the computer it's running on. You can get free-ish X servers (the part of the X Windows system that actually displays the UI) for a Windows machine. (My personal favorite is XWin32, which is not really free, but lets you run for up to 2 hours an unlimited number of times.) You can also use ssh to automatically redirect X connections to the machine you're connecting from. It makes it nearly transparent. And you can do any and all of your command line stuff through that ssh session.

If you're not interested in dealing with it that way, there's a protocol called XDMCP (I believe) that allows you to log in via a GUI console as if you were in front of the machine. It still requires an X server.