Not sure why we didn't think of this years ago, but it's quick and easy to attach a webcam to a balanced arm lamp (from Ikea or Walmart) in order to use as a document camera.
You could also use a flexible arm lamp such as this one.
In both cases I just drilled a 1/4" hole in the hood of the lamp. This allows us to use a 1/4" inch bolt to attach a camera that uses a standard threaded tripod mount. In the above pictures there is just a screw driven into the bottom of the webcam. We have two different higher resolution cameras on order, and we're going to see if we can fit a smaller camera inside the lamp hood for aesthetics.
It's nice to have the option of lighting your subject with the lamp part of this. We use compact fluorescent bulbs, so the hood shouldn't get too hot.
Feel free to comment if you have other ideas for cheap hardware hacks.