Can you play Foster's Home for Imaginary Friends Big Fat Awesome House Party on a different website?

No, you cannot play it on a different website.

Cartoon Network closed it down back in '09 because it was originally supposed to be up for only 6 months, but they kept it on longer.

So now, you can no longer play it, because they took it down.

Sorry!

Hi urmmm yeah, there was a rumour that cartoon network would be bringing back the game in Christmas 2010 but looking at it now. I doubt that it will ever come back... :(