Nothing is forever, and the Grim Reaper takes us all eventually.
This is a relatively rare type of death within the genres we favour at moviedeaths.com, probably because it is generally not too exciting to have a character pass away due to natural causes.
Nonetheless, done properly, Death by Old Age can have a poignancy that is welcomed by an audience jaded by the relentless action during the rest of the film.

And if poignancy is not what is required, a contrived method of rapid aging can always be employed to make someone wither and die before your eyes!

Update: At the time of writing, it would appear that being in a sci-fi / fantasy film, or being a puppet, or both will greatly increase your chances of living long enough to die of old age!