I bought a 2001 Mac Mini last year, partly because I wanted to install it in my car.
Now, however, I don't actually have a car. I don't want to use the Mini as a media center, because I have an Apple TV. I'm currently using it as a monitor stand. It seems a terrible waste. I'd love to make it a brain for a robot hexapod, but that requires more time than I really have.
If worse comes to worst, of course, I'll just donate it to a school or something and bask in the warm glow of good karma. Beyond that, the best idea I have at the moment is dedicated hardware for Archaeopteryx. I can probably set it up to launch with all the necessary software configured and running from boot, so that a monitor isn't necessary, but even then your choice of soundbank is limited without using a monitor, keyboard, and trackpad (or trackball). Other options include some kind of semi-autonomous art installation or home automation.
Get your tweet on if you have any notions.