What are most common natural causes of death?
The WHO has data from 2002 where they have classified and counted causes of death. I have treated the following as natural causes:


Cardiovascular disease (29.34%)
Infectious &amp; Parasitic disease (23.04%)
Cancers (12.49%)
Respiratory disease (6.49%)
Perinatal conditions (4.32%)
Digestive disease (3.45%)
Neuropsychiatric disorders (1.95%)
Diabetes (1.73%)
Genitourinary disease (1.49%)
Maternal conditions (&lt;1%)
Congenital abnormalities (&lt;1%)
Nutritional deficiencies (&lt;1%)
Endocrine disorders (&lt;1%)
Neoplasms (&lt;1%)
Musculoskeletal disease (&lt;1%)
Skin disease (&lt;1%)


I treated the following as non-natural causes:


Intentional injuries
Non-intentional injuries


The sum of the groups explains 96.7% of deaths. I think the remaining 3.3% would be other or undetermined causes, and rounding errors in the data. The natural causes accounted for 87.9%, and non-natural causes were 9.1%. The most common causes were cardiovascular diseases, infectious/parasitic diseases, and cancers. 

It is difficult to assess how natural the cause of deaths are. For example, many cancers, cardiovascular, and respiratory diseases are more common in obese people and smokers (often self-inflicted damage), nutritional deficiencies are often caused by failing welfare and social systems.

Additionally, among the recorded causes of death in England and Wales in 2011, of the total 484,367 deaths recorded, 17,590* deaths were from extrinsic sources (accidents, homicides etc.). This is around 3.6% of deaths. In this data, the most common causes were cancers (29.6%), circulatory diseases 28.8%, and respiratory diseases (14.0%).

According to the CDC, in 2013 there were 2,596,993 deaths in the US, and 92.5% were of natural causes. Of those, the principle causes were heart disease (24%) and cancer (23%). There's a good table at the bottom of this site.

Rates of natural and non-natural causes of death will likely vary greatly by country given different health risks (e.g. malaria in Africa vs Europe), health care services, extrinsic risks (e.g. traffic accidents in Sweden vs India).

$*$ The table in the article features a potential mistake, it seems the columns are incorrectly labelled