I give a short cross-section of select famous-ish arabian/mideast musicians:

Amal Hijazi is fairly atrocious candypop bullsheet (once dubbed "spears of the near east") from Lebanon.

Charbel Rouhana is a famous Lebanese player of the Oud. A good album of his is "Salamat".

Anouar Brahem is a composer and Oud-player from Tunis. A good album of his is "Barzakh".

Hossam Ramzy is a famous Egyptian musician. His "Sabla Tolo" albums (1+2) are some of the best percussion work in the world, EVER. Also he did a pretty neat album named "Immortal Egypt" with Phil Thornton.

Shahram Nazeri is an Iranian musician playing traditional Sufi music, often accompanied by poetry by Jalaluddin Rumi. His very unique style and non-disturbing voice make his music worth a listen. Good album: "Mystified Sufi of Iran".

Omar Faroukh Tekbilek is a very famous and "hip" turkish musician, who however not only plays osman-influenced music, but also makes use of many Egyptian and Persian influences. Quality through the roof. Good albums: "Süleyman", "One Truth", "Fata Morgana", "Mystical Garden", "One".

Deben Bhattacharya's (needs no introduction I believe) famous collection also has a tape "AFGHANISTAN". If you want it hardcore, pick this. Songs like "Goftamash ai Nazaneen" or "Mori eilbandte zome" really bring out the mines on the road to Qandahar. I suggest this as "Arabian/Mideast", because of the notable Persian influences.