Arabian Business magazine does an annual "50 Richest Arabs" list which is a sort of Fortune 500 of the Arab billionaires. (This year they're calling it "the Rich List" and apparently list only 49, the poorest of whom has $1.7 billion.) They include families as units, but don't include the ruling families as such, which of course would make a big difference. The 2010 list is here. Al Waleed bin Talal Al Sa‘ud, the media and property mogul who's also a Saudi Royal, ranks first for the seventh year running with an estimated $20.4 billion. The vast majority are from the Gulf and the Arabian Peninsula; some of the Lebanese and Egyptians on the list also made their fortunes, or parts of them, in the Gulf.
Most of the top 50 are Saudis, Kuwaitis, Emiratis, or Qataris. You'd probably be able to guess two of the three Lebanese: Sa‘d Hariri (No. 27) and ‘Issam Fares (No. 45). Jeweler Robert Mouawad, a diamond merchant, is also on the list at No. 43.
The top ranking Egyptian is the Sawiris Family, at No. 28 ($3.55 billion), centered on telecom and press mogul Naguib Sawiris.
The last two mentions are interesting, though Arabian Business doesn't mention it: they're Christians, as is Palestinian contractor Said Khoury (No. 8 with $7 billion), so three of the richest 50 Arabs are Christian. Robert Mouawad is a Maronite I believe; Naguib Sawiris and his family are Copts, and Said Khoury is Greek Orthodox.
Oh, and one of the richest Arabs seems to actually be a Kurd, but who's counting?