Check out The Online Community Grid.. a grid computing system using Flash Player instances as people browse around the web. I’ve heard rumblings of other projects that ran along these lines, but can’t recall one that was up and running.
The code is up on the Google code thing so you can dig around in it and see what it’s doing.
Some interesting stuff there.. it’s something to keep in mind for later projects and it’s fun to see people continuing to push the boundaries of what Flash is supposed to be.

