I couldn't help but click on this headline story on MSN.com (ok, it wasn't a headline story, but it was on the front page). Amazingly, they can live for about a month without their head. They don't need their heads to breath and ultimately die of dehydration. That's why their indestructable! An entomologist at Delaware Valley College, who carefully decapitated cockroaches, found that although they live for weeks, their learning is quite impaired.
There is an interesting quiz on insects on the Mythbusters page on Discovery.com.