Space Invaders won't move when I use the arrow buttons or space. I'm sure it's not my keyboard because it works with other things.

What browser are you using? :O It works fine for me, I'm using FireFox.

Make sure you're clicking on the flash object. Sometimes (usually) browsers are funny like that and the flash object isn't in focus until you click on it, and if it's not in focus, then the keys don't know they're supposed to be talking to the flash object.