Alright, I think I am getting a better understanding. So what was historically (and in contemporary) the relationship between clans such as the Sauds or Hashemites and the general populace? Was it analogous to the nobility of Europe with the distinction of having been descendant from Mohammed?
How did these tribes or clans originate or form, and how did they retain power over the centuries anyway? It seems to me that unlike the nobility of Europe where only the main line is relevant, all members of the family and all their descendants form part of the clan. (Also did they only marry within their own clan? With clans of similar prestige?) What role did these families have in the expansion of Islam and Arabinization of the Middle East/North Africa?
I know I am asking a lot of questions but I feel you are the right person to ask so I might as well get them all out.
Meh, I'm not exactly an expert on the Middle East at all. Modern Israel, maybe, but not the rest of it by a long-shot. I'll try though.
Most of the famous Arab families trace their descent from the family of the Prophet, if not from him directly. Only the Hashemites actually have any degree of verification for this claim. The Saudis are something of an exception to this; they've only been around since the fifteenth century and only became prominent in the eighteenth, and to my knowledge have never once claimed descent from the family of Mohammed. They were basically a prominent family in a local tribe on the Arabian Peninsular who had a knack for the tribal warfare that was a constant there. Their primary enemies were the Sharif of Mecca, who were the main branch of the Hashemite family and the traditional rulers of Mecca (under Ottoman suzerainty). I've already mentioned how the Sauds defeated the Hashemites in the post-WWI war on the Arabian Peninsular.
Most of these large Arab families are more akin to clans than actual families, and yes, there is a lot of marriage within the family. Richard Burton - the explorer, not Elizabeth Taylor's husband - famously said that an Arab considered his father's brother's daughter (ie, his first cousin) as his betrothed, and there's some truth to that. Cousin-marriage does seem to have been fairly common, though not as much as Burton implied. I believe it's official Saudi policy to marry within the family to keep the wealth there, but with a family of 12,000 or more, that doesn't exactly limit a person's options.
Traditionally, most of the peoples on the Arabian Peninsular were nomadic and tribal, so marrying within the tribe was virtually required. The conflicts between nomads and sedentary populations is a staple of Arabic folklore for a reason; it existed for the entirety of their history, and still does to an extent. Mohammed was somewhat unusual in that he was a city-dweller who led one city to triumph over another, rather than a nomad doing so.
Most of the prominent Arab families are either fairly new, like the Saudis, or have been in power for a long time, like the various sheikhdoms in the UAE. They didn't really have much to do with the great Islamic expansion; even the Hashemites tended to stay behind as the rulers of Mecca itself, and while every caliph before the Ottomans claimed descent from Fatima, pretty much none of them after Ali's death actually did. Not even the Fatimids themselves, apparently.
These prominent families tend to marry within their own family or within a similar social class, but there's no set-rule. Remember, Islam condones polygamy, and most Arabic leaders are Muslims, at least in name, so they tend to take multiple wives. It's far from uncommon for a sheikh to take one wife from his own extended family, a second wife from an allied royal line, then simply take a couple of young hotties he found while out hunting as his third and fourth wife. He was also traditionally allowed one female slave for his own personal use, so buying another young hottie from her parents as more of a fifth wife than a slave was also pretty common.
Among the lower classes, one wife was the norm, with an occasional second. I am unsure of the legality of marrying sisters, but it was pretty common regardless. The Muslim half of my great-grandmother's village used to marry two or even three sisters to the same man pretty regularly, usually because the sisters refused point-blank to be separated.