Well, one's a simulator, but, anyway...
Some Canadian dude wrote a BASIC simulator, and a ZX-81 emulator. On his page, there are also sample programs people have submitted, including games. I thought it might be worth looking at, at least for a few minutes.
I'll just go ahead and post the links.
http://www.vavasour.ca/jeff/level1/simulator.html
http://www.vavasour.ca/jeff/ts1000/index.html
EDIT: Ooh, and check this out. Made by the same guy.
http://www.vavasour.ca/jeff/popup.html
I was going to take the pop-up challenge, but I realized my browser prevents them. :D
Shut it off for the site, then.