When you are young your body constantly regenerates and rebuilds the body when it becomes damaged however as life goes on the body becomes less able to deal with this and things that previously wouldn't have effected you now do.
This means that you don't die of old age but the body just becomes unable to deal with problems it has.
This is similar to AIDS, people don't die of AIDS but die of an illness which the body is unable to fight because AIDS destroys the bodies ability to fight infection.
A common killer of the old and people with AIDS is Pneumonia
http://www.reutershealth.com/wellconnected/doc64.html