In my study of Middle Eastern percussion (I play the doumbek, aka the derbouka), I have had the privilege of getting to know some of the classic songs that people in the Middle East have grown up with.
To mention some favorites of mine: among the works of the famous Umm Kalthoum, I love the song "Ana Fi Intizarak""). It's been remade many times by different people.
I also love to listen to the smooth voice of Farid Al-Atrache (the spelling varies on his name). Any of his works. His voice is expressive and serene at the same time.
Another favorite song of mine, which I have only heard as an intsrumental, is the lively "Qariat Al-Finjan" (The Reader of Tea Leaves). Very fun to drum to!