Algeria:

Office National des Statistiques (الديوان الوطني للإحصائيات = al-Dīwān al-Waṭanī lil-Iḥṣāʼīyāt, National Office of Statistics)

Comprehensive national statistics site. Data is presented in downloadable .pdf files. French.

Bahrain:

Central Informatics Organisation (الجهاز المركزي للمعلومات = al-Jihāz al-Markazī lil-Maʻlūmāt)

Comprehensive national statistics site. Also provides citizen services (identity cards, etc.) and GIS information. Data is presented in downloadable .pdf files. English and Arabic.

Egypt:

Central Agency for Public Mobilization and Statistics (الجهاز المركزى للتعبئه العامه والإحصاء = al-Jihāz al-Markazī lil-Taʻbiʼah al-ʻĀmmah wa-al-Iḥṣāʼ, CAPMAS)

Comprehensive national statistics site. Data is not downloadable. Arabic only.

EgySocialData (مشروع البيانات المصرية = Mashruʻ al-Bayānāt al-Misrīyah)

Online open-access platform for for social data in the Egyptian context. Site includes reports in English (downloadable in .pdf format) and statistical data in Arabic (downloadable Excel spreadsheets).

Iran:

Statistical Centre of Iran (مركز آمار ايران = Markaz-i Āmār-i Īrān)

Comprehensive national statistics site. Data is presented in downloadable Excel spreadsheets. English and Persian.

Socio-economic Data (SSRC, Princeton, Syracuse)

Via the Iran Data Portal. Various ministries, bureaucratic institutions and state-affiliated research centers of the Islamic Republic of Iran regularly publish socio-economic data. This resource provides English translations of some of this data in individual Excel spreadsheets, indicating the data source at the bottom of each individual spreadsheet. Other data is provided in the form of downloadable .pdf files.

Iraq:

Central Statistical Organization (الجهاز المركزي للإحصاء = al-Jihāz al-Markazī lil-Iḥṣāʼ)

Comprehensive national statistics site. Data downloadable as .pdf files; the Arabic section has more information. English and Arabic.

Jordan:

Department of Statistics (دائرة الإحصاءات العامة = Dāʼirat al-Iḥṣāʼāt al-ʻĀmmah)

Comprehensive national statistics site. Data is not downloadable. English and Arabic.

Kuwait:

Central Statistical Bureau (الإدارة المركزية للإحصاء = al-Idārah al-Markazīyah lil-Iḥṣāʼ)

Comprehensive national statistics site. Data is downloadable as .pdf files; some newer data is available in downloadable Excel spreadsheets. English and Arabic.

Saudi Arabia:

General Authority for Statistics = الهيئة العامة للإحصاء (Saudi Arabia)

Comprehensive national statistics. Data presented in downloadable Excel spreadsheets and .pdf files. Most data is in both English and Arabic, although some is in Arabic only.

GASTAT Portal (Saudi Census) 

A comprehensive census providing a complete and accurate count of the population along with information on housing, across all locations in the Kingdom and sub-groups of the population. Data in Arabic & English, downloadable as .csv & .pdf files.

Turkey:

TurkStat (Turkish Statistical Institute, Türkiye İstatistik Kurumu)

Presents comprehensive data, downloadable as Excel spreadsheets. English and Turkish.

Multicountry:

Arab Barometer (ICPSR, Ann Arbor, Michigan)

A multicountry social survey designed to assess citizen attitudes about public affairs, governance, and social policy in the Arab world, and to identify factors that shape these attitudes and values. Respondents came from Algeria, Egypt, Iraq, Jordan, Lebanon, Palestine, Saudi Arabia, Sudan, Tunisia, and Yemen. The project's website provides additional content and tools for analysis.

Data Catalog (Economic Research Forum, Cairo)

National statistics for Egypt, Palestine, and Jordan. Also includes some statistics for Iraq, Lebanon, Morocco, Somalia, Sudan, Tunisia, Turkey, and Yemen. Data available from 1995 on. Most documents are presented as .pdfs with some Excel spreadsheets. Mostly Arabic.

UN/ESCWA (Economic & Social Commission for Western Asia)

Key documents & virtual library for economic & social statistics for Algeria, Egypt, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Oman, Saudia Arabia, Sudan, Syria, Tunisia, United Arab Emirates, and Yemen. Documents presented in .pdf or .html format in English, Arabic, and Spanish.

Eastern Mediterranean Regional Health System Observatory (WHO)

The RHO data repository provides access to over 50 datasets on priority health topics including mortality and burden of diseases, the Millennium Development Goals (child nutrition, child health, maternal and reproductive health, immunization, HIV/AIDS, tuberculosis, malaria, neglected diseases, water and sanitation), non communicable diseases and risk factors, epidemic-prone diseases, health systems, environmental health, violence and injuries, equity among others. Data is not downloadable. English.