In 1940, the Russians were apparently able to, among other things, keep a dog's severed head alive. This flick from the Internet Archive details the whole shebang. We think it's fake, personally, because otherwise someone would have used the technology for people's pets by now.

"Sure, it's only Fluffy's head on a plate, but it was either that or we would have lost her for good. Sure she can't run around anymore. But she still purrs. Oh, and she can headbutt some yarn like nobody's business."

You smirk. But even as you do, you're thinking of some cat lover you know who would do it. Here's a Wikipedia article with more info.

Found via Futurotica.