I think the body just wares out. Or to quote Stewy: "The only reason we die - is we accept it as an inevitability."
Because if everyone was still alive, Earth would soon be overrun and life would be a horrid, miserable mess. We would run out of food, water, and resources. Animals would gore humans, humans would attempt to destroy humans and animals, but nothing would actually work because none of us could die so eventually we'd all plunge ourselves into an unending world of irreperable pain, and as the population continued to increase, we would soon literally find ourselves buried under bodies, suffocating, wounded, dying, but never dead. And that would totally suck.
^^ Thats a good reason why we SHOULD die. His reason was why DO we die. And that reason is that humans aren't built to live forever. That's all there is too it.
Death is necessary. Imagine getting your head crushed, but still surviving... no thanks. As for dying from age, the medical reason is because our DNA is constantly being renewed by our bodies, but once we've reached our prime, small degredations form with each renewal. It's the classic "copy of a copy of a copy" scenario, where the flaws compound with time. These flaws are what cause aging. No doubt our bodies trigger these flaws by intention to control population limits, but it is entirely possible (although just outside our current technological advancement) to stop the proces by gene therapy, forcing the body to renew DNA without defects. One day people could potentially live forever. Scary, no?
Well luckily I used the qualifier "potentially" Hooray! If the human race goes extinct, my previous post will technically still be correct. Phew.
Because if there was no death, Satan would be on his throne going like, "Bummer." And God would get bored and go make some other place where the dominant race are moving sunflowers.