I am an American of European descent, but I play the doumbek (a.k.a. tabla/darbuka) and am starting to learn riq (tambourine).
There are a lot of different styles of music. I'll tell you about different styles I am familiar with. However, I don't know if people from the Middle East would break things down into the same categories as I would. Let me know if you see it differently because I am interested to know what other people think!
Muwashshah: old-style music that uses the semai rhythm quite a lot. Semai is a 10/8 count; I've heard it described as being like a long waltz. I think muwashshahat sound formal and very pretty.
Egypt beledi: I think beledi means "country". They use certain songs (e.g Hassan ya kholy el genena) and taqasim (improvisations). It sounds earthy and relaxed and is something I'd want at a party.
Saidi: Happy music with what I call "the horn" (I think it's called a mizmar). It reminds me of beledi music with its earthy feel. There are great stick/cane dances to this style.
Taqasim: Some songs are almost all taqasim (improvisation) often without singing. Taqasim music makes me think of oud players.
Debke (or debkah?): I believe debke means "stomp"? People do fantastic line dances to this music that I REALLY want to learn! This also sounds like party music. I understand that it varies by country. There are distinctive drum rhythms that are used in debke music (4/4 maloub, 6/8 Lebanese-debke, etc.).
Golden era music: Om Kolthoum, Farid El Trache, Mohammed Abdul Wahab, Abdel Halim Hafez
Beautiful, classic music from about the 1950s to 70s. Om Kolthoum and Wahab songs tend to have lots of rhythm changes that create a dynamic feeling. I think this music is very emotional; Om Kolthoum can make me cry!
Shabbe: I think it sounds like modern pop music with a middle eastern vibe. Fun music, but they don't tend to change the drum beat very much.
Modern Arabic pop: To me, it sounds like American music with Arabic lyrics. They often use the same drum beat throughout a song, which I think gets boring.
What is your favorite kind of music? I am curious to hear what other people think.