The New England Journal of Medicine has looked back through 200 issues  and come up with this - a handy chart telling us how we currently die (compared to ten years ago).
Well, mortality rates have dropped, thanks to the massive reduction in infectious diseases, so that's good. Cancer, on the other hand, has got much worse - the mortality rate almost doubling. We have fewer fatal accidents, but more suicides; no Diptheria, but more noninfectious airway disease; and, on a semantic note, Alzheimer's disease instead of "senility".
But more differences emerge when we look further back in time.
Back in 1812, it turns out spontaneous combustion was taken quite seriously. Here's the New England Journal report:
Reports of spontaneous combustion, especially of “brandy-drinking men and women,” received serious, if skeptical, consideration.
In a 1912 issue of the journal, one article noted a new problem, "automobile knee" which afflicted “persons of extremely indolent habits of life” who no longer walked more “than the few steps that are needed from the chamber to the elevator, from the elevator to the dining-room, or lounging-room, and then to the automobile”.
The report notes however that at least one editorial from that year was a little off the mark:
One editorial, describing progress made since the Journal's early years, rhapsodized about what another century of medical discovery might bring: “Perhaps in 1993, when all the preventable diseases have been eradicated, when the nature and cure of cancer have been discovered, and when eugenics has superseded evolution in the elimination of the unfit, our successors will look back at these pages with an even greater measure of superiority”.