There are numerous projects for digitizing Middle Eastern newspapers. The projects highlighted here have digitized periodicals from the Land of Israel\ Palestine:
Digital collection of the British official gazettes for Palestine, 1919-1948.
Project: Arabic and Middle Eastern Electronic Library (AMEEL) – Yale University (Gazettes and Journals).http://findit.library.yale.edu/catalog/digcoll:2835720
Digitization of 24 historical periodicals (1900-1950), primarily from Palestine, from the al-Aqsa Mosque Library in East Jerusalem. Project: Endangered Archives – British Library.http://eap.bl.uk/database/results.a4d?projID=EAP119
Digital collection of the historic Jewish and Hebrew press, including 5 Hebrew periodicals from Ottoman Palestine and 12 Hebrew and English titles from Mandatory Palestine. Project: JPress: Historical Jewish Press website of the National Library of Israel and Tel-Aviv University. http://www.jpress.nli.org.il