There are a lot of cheap ones that are designed for the purpose on ebay, just search for 'dash cam'. They take standard SD video, record to an SD card and overwrite the oldest videos as it runs out of space. They can also start up automatically when they get power/you turn on the car. And they have a monitor.
I'm thinking of buying one of those Raspberry Pi cameras when they become available and whipping up a bit of Go code to make my own dashcam for < $100. I think it would work great. You could even add a cheap USB wifi dongle and have it upload the videos when you're in your driveway.
I've installed these in taxis. They have outside/inside cams (to make sure the occupants aren't pointing a gun at the driver). They have a wireless 2.4ghz wireless upload to upload the files when the car gets to home base. And they show telemetry, speed, gps, and impact/vibration.
They are for commercial purposes so they are probably out of the price range of most people ($400 I think).
I've been eyeballing a GoPro for a dash cam since it also overlaps with my other hobbies (cycling and ATV riding). The big drawbacks seem to be the low-light filming and the fact that it doesn't automatically turn on or automatically rewrite when the disk gets full.
Can anyone here recommend a brand/model?