Which countries are still ruled by sheikhs?

Technically sheikhs include many other esteemed men besides rulers, though the main areas of what the west call sheikdoms are in the Gulf States such as United Arab Emirates, Qatar and Kuwait as well as East Africa

https://en.wikipedia.org/wiki/Sheikh

Technically the rulers of Kuwait, Bahrain, Qatar and United Arab Emirates are called emirs. Is an emir the same as a sheikh? By the way, the ruler of Oman calls himself a sultan. Where in East Africa would you find a sheikh as the present ruler of an independent nation?

Some of the members of the Islamic Courts Union in Somalia who control parts of the country call themselves "sheikhs", but they are not (yet?) the official rulers of Somalia.

Sheikh is more an honorific title than a title belonging to a ruler as such. You can be a sheikh and an emir or sultan at the same time. And you can be a sheikh without ruling anything. The individual rulers of the Emirate states are all sheikhs https://en.wikipedia.org/wiki/List_of_rulers_of_separate_Emirates_of_the_United_Arab_Emirates and one of them who holds a doctorate as well just happens to be called Sultan (as a name) to confuse matters!), and the President of the UAE is also a sheikh. But they rule as Emirs.