Here's tonight's very hacky project, a VNC Server running on an Arduino Ethernet board.
Here's the Arduino Ethernet VNC Server code and information.
Here's a screenshot of the sample output, it can also make your computer beep and write text to the clipboard:
Still need to work on the input side of things and make the code less cringe-worthy.
I was quite impressed with a few hours work and ~5KB compiled--including the original, larger, Ethernet library and some very inefficient code.
P.S. This does require one patch to the Ethernet library to enable detection of a client which has connected but not yet sent data. This is really a "missing feature" which should be implemented properly, rather than my quick fix. :-)