I bring this up all the time, and most of the non-hunters will be shocked at how good game cameras are...They also have protective housings that you can purchase so they don't get stolen or damaged. (Many people hunt public land, you'd be surprised what people will do when nobody is looking).
Remember, these things take pics and video of deer in the middle of the night..There aren't any streetlights in the woods.
Lastly, many of the better ones have the ability to send video and images directly to your mobile phone for $15 per month, and because they're for hunting you can turn that service off whenever you'd like.
Here are 3 brands that I'd recommend.
Bushnell. (Good quality, stand by their product. most of my personal cams are Bushnell)[Link: bushnell.com]
SpyPoint. (Popular work great, inexpensive).[Link: spypoint.com]
Reconyx (In my opinion, best camera on the planet, built like a tank, but expensive).[Link: reconyx.com]