The Apple Macintosh is the most well known example of GUI design, but it's conceded that Xerox gave them a head start. Interestingly, though Xerox spend most of the resources developing its 'Alto', what should be considered the forerunner to the modern user interface, they pretty much gave it away to Apple.

Interesting note: Apple eventually hired away several of the Xerox's PARC engineers to work on the Lisa GUI, that's how impressed they were.

http://home.san.rr.com/deans/lisagui.html
A short timeline of the development of the Apple GUI




GUI design, describes, as daglo said, the look and feel of the program's interface. However, interface design encompasses the way the user interacts with the program, as well as the program's appearance itself. Apple wasn't just designing the graphical component of the computer, they were also describing how the user would interact with it, in terms of physical components (the mouse, specific keyboard keys, arrangement of case hardware).

And we have Douglas Englebart to worship for that, thank you.

http://www.inventors.about.com/science/inventors/library/weekly/aa043099.htm
Invention of the modern computer interface (at About.com)




Of course, we know what happened later. Microsoft 'innovated' the Windows GUI from the Apple GUI, and several incarnations later we have what I suppose is what is considered the interface standard, Windows 2000. I don't expect Microsoft to change their GUI much, due to their dependence on the novice user base for much of their revenue, but that doesn't mean that we can't continue to improve upon it:

Litestep
Darkstep
WindowBlinds
eFX
Chroma
CustomEyes
Daya
Illumination

www.deskmod.com
www.skinz.org