The people at Mac Mini Vault have managed to set up a webpage that's hosted on a jailbroken Apple TV 2G. You can check it out here. They do note that "it will never be a sustainable service to offer."
Still they say it was a fun project that allowed them to see how far they could take the little machine. As website 9to5Mac points out, the Apple TV is very lightweight when it comes to power consumption. It's powered by the A4 chip (as are the iPhone 4 and original iPad). Mac Mini Vault is also keeping an eye on the machine as they monitor the CPU load.
Interesting little experiment. They have some hints for anyone wanting to do the same. If you want to jailbreak Apple TV and give it a shot, check out their instructions here.