Cockroaches stay alive after you cut the head off!

The reason an organism dies when the head is cut off is because the brain stops regulating the body's functions. The simpler the organ, the less the brain actually has to do. So when a human's head is cut off, all the organs basically start shutting down. The head dies in like thirty seconds because it isn't receiving oxygen through the blood and the body dies in a similar time (I think) because there's nothing regulating it's functions.

On a cockroach, The cockroach brain is spread throughout its body. The head holds a bit of a nervous system, while the rest of the brain is scattered along the ventral (belly-side) part of its body. So, now you understand that if you cut off the head of a roach, it will still live for as long as one week; eventually dying from starvation or thirst