Here's the first Arduino based project, or at least developed on an Arduino.
RWAP and bought one. They are very good replicas, the only noticeable difference I could see is the © date at the top, 1980 vs 2008.
Arduino USB Library seems to be in good order, a port of V-USB, and little is required to get a USB keyboard up an running. I built the circuit on a propto shields and added some keys on breadboard. The major stumbling block for me was most of the sample circuits on the net used pins D2 and D3, where as the config file supplied used D2 and D4. Once I'd changed that, my little 6 key keyboard was up and running. I also tested it with the new membrane and that was working as well.
I was probably watching the same thing the last time I used the original ZX81, just on a slightly smaller TV.
Post with source and description
Post with schematics
Arduino Leonardo based ZX81 USB keyboard
ZX81 USB Keyboard by Dave Curran is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License