The Kingdom of Saudi Arabia staunchly follow Wahhabism, a very conservative and strict brand of Islamism that probably is the major factor of Saudi's strict policy and harsh implementation of Sharia. How did it become so? According to Wikipedia, it began by an alliance between theologian Muhammad ibn Abd al-Wahhab (the father of Wahhabism) and Muhammad ibn Saud (the founder of the Saudi dynasty), when ibn Saud tried to fight the Ottoman Empire and found the First Saudi State in the 18th centuries.
However, it's been centuries (and generations of rulers) since then, and also Wahhabism isn't very popular in most of the rest of Muslim world, but it is interesting to see that they remain strong in Saudi Arabia, supposedly influencing the decisions and policies of its absolute rulers. How did it become so?