Most everyone has a digital camera these days and a lot of those cameras have video capability as well. Here’s a fellow who came up with a quick and cheap way to mount a camera on your motorcycle’s handlebars with a bit of plastic pipe, garden hose and hose clamps.
Nothing fancy but very functional and sometimes that is all you need. It would probably work with most digital video cameras as well. There are lots of very special, purpose built camera mounts out there, but making one from things you probabaly have in your garage or basement workshop is neat.