Actually any country that has as its constitution the Qur'an has and is following Islamism. That means that most of the Arab countries in the Middle East are following Islamism.
I am going to go out on a limb here and say I don't believe there are any countries which have as a constitution the Qur'an. Do you really mean that there are countries which include Sharia as part of their constitution?
The Constitution of Saudi Arabia Chapter 1 General Principles
Article 1
The Kingdom of Saudi Arabia is a sovereign Arab Islamic state with Islam as its religion; God's Book and the Sunnah of His Prophet, God's prayers and peace be upon him, are its constitution, Arabic is its language and Riyadh is its capital.
<SNIP>
Article 7
Government in Saudi Arabia derives power from the Holy Koran and the Prophet's tradition.
Article 8 [Government Principles]
Government in the Kingdom of Saudi Arabia is based on the premise of justice, consultation, and equality in accordance with the Islamic Shari'ah.
The Constitution of the Republic of Yemen Chapter I: The Political Foundations
Article (1) The Republic of Yemen is an Arab, Islamic and independent sovereign state whose integrity is inviolable, and no part of which may be ceded. The people of Yemen are part of the Arab and Islamic nation.
Article (2) Islam is the religion of the state, and Arabic is its official language.
Article (3) Islamic Shari'ah is the source of all legislation.
The Constitution of Egypt Egypt.Constitution
Chapter one: The State
Art.1*: The Arab Republic of Egypt is a Socialist Democratic State based on the alliance of the working forces of the people. The Egyptian people are part of the Arab Nation and work for the realization of its comprehensive unity.
Art.2*: Islam is the Religion of the State. Arabic is its official language, and the principal source of legislation is Islamic Jurisprudence (Sharia).
The Constitution of Syria Article 3 [Islam]
(1) The religion of the President of the Republic has to be Islam.
(2) Islamic jurisprudence is a main source of legislation.
The Constitution of Bahrain Article 2 [State Religion, Shari'a, Official Language]
The religion of the State is Islam. The Islamic Shari'a is a principal source for legislation. The official language is Arabic.
The Constitution of Oman Article 2 [Religion]
The religion of the State is Islam and the Islamic Shariah is the basis of legislation.
I think the limb you were on rporter314 just broke. When I talk about Islamists and Islam I know what I am talking about. The only Arab country that DOES NOT the Qur'an and sharia as the basis for its laws is Lebanon.