Here's my video set up. Well, a couple of them at least:
Setup #1: Sony Handycam DCR-SX85 Camera and a basic tripod I got from Wal-Mart, with a bit of camouflage duct tape to cover some of the more reflective areas.
This is what I use most often when hunting solo. The tripod is very steady, and it leaves my hands free when I need to make a shot. This camera has an impressive 70x zoom capability, which means I can capture decent video of game at ranges in excess of 300 yards.
Setup #2: Sony Handycam DCR-SX85 and a monopod.
If I'm going to be accompanying someone hunting and focus solely on filming, I use the Handycam and monopod. It's not quite as stable as the tripod, but it's much lighter and much less bulky, making it a better choice for crowded tree stands or ground blinds.
Setup #3: Midland XTC-100 action camera with a bicycle handlebar mount.
This is my action camera, which I place on long guns, my crossbow, and my compound bow. While not nearly as good as a Go-Pro, it still serves its purpose. None of the mounts are particularly suited for these types of setups, but I make them work. It takes a few seconds for the camera to start recording once turned on, but I've captured some neat duck hunting and clay shooting footage with it on my shotgun.