The GoPro HD camera can be mounted to many, many things--helmets, surfboards, and cars. Apparently it's also small and lightweight enough to hang around your cat's neck. The movie above, which says it's the first movie filmed by cats, was shot using the GoPro HD and for a camera designed for shooting outdoors it handles indoors/low-light conditions quite well.
This movie was inspired by the results from a study conducted by Nestle Purina PetCare's Friskies brand. For that, 25 cats wore specially designed portable video cameras around their necks to capture daily clips for five days. The "specially designed camera" used is called the Eyenimal, which unfortunately isn't readily available in the United States (I found it online for $135 or you can order it from the manufacturer in France for $168.)
The video from the Eyenimal is VGA recorded in AVI format, but the results are actually decent considering most of the movies are indoors under less than ideal lighting and dangling from the neck of a cat. Not as nice as the GoPro's but still good and if you want a dedicated camcorder for your pet, the Eyenimal is cheaper. It can shoot for up to 2.5 hours on a single charge, storing to 8GB of internal memory. USB is used for charging and transferring video off the device. (The big takeaway from the study, by the way, is that cats are social despite their reputations.)
While the study is great, I'm mostly interested in the technology. It's stuff like this that makes me think about how easy and cheap it's gotten to shoot video. My first camcorder was a PXL-2000, a toy that recorded black-and-white video to audio cassettes. Now, you can shoot good 480p video with something like this $25 Micro Camera that fits on a key chain and records to microSD cards. Crazy.