18, but I think it varies according to the countries since you need to be 21 to become an adult in Japan.
It varies from country to country.
For the great majority of countries including most of Europe it is 18, although it is only 16 in Belgium and France.
It is 20 in Japan.
In the USA the federal minimum age is 18, although states are free to raise it. Alabama, Alaska, New Jersey and Utah have raised the minimum age to 19.
The highest age limit in the world is in Montenegro where cigarettes cannot be purchased by anyone under 25. The lowest is Bangladesh where the limit is 15.
The above discussion excludes many of the poorer African nations where there are no effective controls on tobacco.