Big question, but I'll try and answer it as briefly as possible.
In the Islamic Middle-East, armour was never quite as widespread as it was in Western Europe, but it was used, particularly by elite and professional troops, emirs, tribal chiefs etc.
At the time of the prophet (circa 570-632 AD) and for the first century or so afterwards, mail hauberks, quilted armours and leather armours were dominant. During the time of the prophet armour was rare, but once the Great Arab conquests got underway armour was pretty common as the Arabs captured vast amounts off the Eastern Romans and Sassanid Persians. The Arab Empire under the Ummayads and early Abbassids was also one the wealthiest empires in the world and as a result their troops would have been very well equipped.
The Abbassids started replacing their Arab troops with Iranian and Turkish troops who were seen as less likely to rebel than Arab tribal warriors, and this is when Lamellar armour probably started being used by Muslim warriors. In North Africa lamellar armour never took root, although after the Ayyubid takeover of Egypt it was used by Ayyubid and later, by Mamluk troops.
Up until the late 14th century mail and lamellar were the dominant armours in the Middle-East. In the late 14th century mail-and-plate armours appeared, with the "krug" appearing in Mamluk Egypt in the late 15th century. In the late 14th century, the Mamluks and Iranians also started using brigandines and "faux brigandines", probably as a result of Mongol influence (after their conquest of China the Mongols started using brigandines. Interestingly coats-of-plates first appear in Western Europe in the 2nd half of the 13th century; the Mongols defeated the Poles at Legnica and the Hungarians at Mohi in 1241...)
In the 15th century the armours used by the Ottomans, the Mamluks and Iranian warriors were very similar. This changed in the 16th century; The Ottomans conquered Mamluk Egypt in 1517, then in the late 16th century Ottoman and Iranian weapons and armour diverged. the Ottomans continued to use armour similar to the types used in the 15th century up until the 2nd sige of Vienna in 1683, where as from the early 16th century the Iranians started using simpler and more elegant types of armour and helmets like the so-called
kulah-khud helmet and
chahar ayna cuirasses over mail Hauberks. In the late 16th and 17th centuries The armour of the Mughuls of India was under both Ottoman and Iranian influence, although the Iranian influence was always stronger.
Russian armour was strongly influenced by both Persian armour from the late 14th until the late 17th centuries. This was probably as result of Mongol Rule as by the late 14th century the Golden Horde were using Iranian style armour.
During the 16th and 17th centuries the Poles and Hungarians used a mixture of Western European and Turco-Persian arms armour (previously they had used exclusively Western European styles). 17th century Polish hussars for example used Turkish style
chichak helmets, vambraces and curved sabres with Western European style cuirasses and pauldrons. Polish
pancerni cavalry on the other hand were very Turkish in appearence.
Here some previous posts of mine with pictures of Middle-Eastern and Eastern European armour (you might have to scroll down a bit):
http://forums.taleworlds.com/index.php/topic,1341.msg338758.html#msg338758
http://forums.taleworlds.com/index.php/topic,1341.msg307916.html#msg307916
http://forums.taleworlds.com/index.php/topic,1341.msg270381.html#msg270381
And various armours:
Mamluk, Ottoman, Iranian and Mughul:
http://i4.photobucket.com/albums/y110/Nephtys/Oriental/Kulah_khud_Iran_19th_c_1.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental/Ottoman_chichak_1.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental/Turban_Helmet_15th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental/Mamluk_helmet_Egypt_15th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental/MdHuK_Krug.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental/Mughul_Armour_VA_1.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/MS_39.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/Cuisse_Iran_or_Anatolia_15th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/shirt1.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/shirt3.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_296_vambrace_iran_16th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_cuisse_mamluk.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_greave_03.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_helmet_turkey.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_mail-and-plate_armour_Iran.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_turk_helmet_002.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/acpi_visor_iran.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/ACPI_Indian_shield_15th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/ACPI_Turkish_cane_shield_16th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/ACPI_Quiver_Bowcase_17th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Oriental%20Warriors/**-qoyunlumail-and-platearmour15thC.jpg
Russian and Polish:
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Rushelmetearly12thc.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/AN_helm_01.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Pancerni_armour_01.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/MdHuK_59_Hussar_equipment_1556.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Polish_Zischagge_002.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Hussar_cuirass_17th_C.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Bechter.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Rushelm17thC.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Zertsalofrontandback.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/mail--PlatearmourRus17thc.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/HelmetRus17thc.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/mail--PlateshieldandvambraceRus17th.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/karacena003.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/karacena004.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Hussar_armour_circa_1630_001.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Hussararmourcirca1630_002.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Hussararmourcirca1630_004.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/MdHuK_48_Hungarian_armour_1560_AD.jpg
http://i4.photobucket.com/albums/y110/Nephtys/Medieval%20European%20Armour/Eastern%20Europe/Hussar_armour_01.01.jpg
Hope that answers your question!
