Response to Starslab's question. Response comments have a stupid length limit, so I'll just make a new post.
You can use this map for reference in the following post:
The UAE is divided up into 7 internal divisions, called emirates. The three largest emirates are Abu Dhabi, Dubai and Sharjah. The remaining four (Ajman, Umm al-Quwain, Ras al-Khaimah and Fujairah) are significantly smaller and are often collectively referred to as the "Northern Emirates." Each emirate has a capital city of the same name. On the map above I have indicated the cities of Abu Dhabi, Dubai and Sharjah (Al Ain is included for reference; it is where I used to live in the early 90's) as well as their respective emirates. Emirate boundaries are marked by the darker green lines.
Abu Dhabi (the city) is the capital, and (the emirate) is also by far the largest -- as you can see on the map, it comprises about 80% of the land area of the UAE. Accordingly it has about 90% of the oil (most of the remainder belongs to Dubai) and thus drives a significant part of the UAE's economy. It is also the only emirate with a second city (ie: Al Ain) of any significant size. Politically it has the most weight in the Federation.
The four largest cities in the UAE are Abu Dhabi (800,000), Dubai (800,000), Sharjah (500,000) and Al Ain (300,000). These numbers are estimates at best, as no comprehensive, accurate and consistent census has ever been taken (due to political reasons more than anything else -- that's a whole different discussion). For comparison, all of Greater Vancouver is about 2.7 million, which is co-incidentally almost the same as the UAE's combined population.
The cities of Dubai and Sharjah, as can be seen on the map, are very close to each other, and have a similar relationship to Seattle-Tacoma. Or, um, Vancouver and New Westminster (sort-of... that analogy is a lot weaker). This makes the Dubai/Sharjah/Ajman (Ajman being that little enclave immediately north of Sharjah, and has about 50,000 people) conurbation the largest city in the UAE, although due to the emirate divisions within the urban area, it's not anywhere as cohesive a city in terms of infrastructure, public transit, property laws, etc as would otherwise be the case, and are often treated as separate cities (think Detroit/Windsor). This is also partly due to the huge wealth gap between Dubai and Sharjah/Ajman.
My parents, as have been noted, live in an apartment in Abu Dhabi, right in the center of town. It is about a 5 minute walk to the ocean and 10 minutes to downtown.
I live on campus at AUS. If you look at Sharjah on the map, you will notice a road heading directly east, over to the mountains and the east coast. AUS is about 20km east of the town center along that road.
The 7 emirates exist as largely autonomous political entities. The UAE was formed in 1971 as a result of Britain (who had previously occupied most of the region) suddenly pulling out (with, like, 6 months' notice) and leaving the area to fend for itself. Prior to the federation, each of the emirates was a largely independant kingdom (or sheikhdom, as they also used to be called), along with Bahrain, Qatar (who are now independant countries) and the now defunct Kalba. The various sheikhdoms have a long, long history of petty squabbles and minor wars. This exists today in the form of an eternal pissing contest between Abu Dhabi, Dubai and Sharjah, but there is more unity than not. Which has been a great surprise to most observers. When Britain pulled out, the emirates that are now the UAE decided they were stronger together than apart and came together in a loose federation.
(As an aside, a lot of this is due to the ruler of Abu Dhabi, and the UAE's president, Sheikh Zayed. He has been far stronger than the remaining rulers, and thus the uncontested ruler since 1971. There is some concern over what will happen when he dies -- as he is already in his late 80's. There is a significant chance that the ruler of Dubai will contest Zayed's son's unilateral right to become president.)
As alluded to, the various emirates are monarchies in the strictest sense of the word. Each has its own ruling family, where the right to rule is passed down from father to son. The UAE in general is a federation, basically made up of representatives from each of the 7 royal families, who elect a leader from amongst themselves (which as I indicated has to date always been Sheikh Zayed of Abu Dhabi), and appoint a board of advisors. In theory these advisors can be anyone (as long as they are a UAE national), but in reality they almost always come from one of the ruling families. The same is true of the various ministers (ie: minister of education, minister of public works, minister of defense, etc). Again, Abu Dhabi has the most clout in the government, followed by Dubai.
As I started out by saying, the various emirates have a great deal of autonomy, mainly for historical reasons, although as time goes on and the ruling families trust each other more and more, there is ever more cohesion. Once (that is, if) the issue of Zayed's succesor is settled in a way acceptable to everyone, the feeling is that we can probably expect this process to accelerate.
So, what is done in co-ordination? Basically, defense, foreign policy, education and health care (and to a certain extent, transportation) are centralized. And there's transfer payments to the poorer emirates from the federal government (as only the three major emirates have oil, the remainder exist solely on federal handouts, and there's a HUGE wealth gap...) and that's about it. Pretty much everything else is done independantly.
In terms of internal policies, Abu Dhabi, Dubai and Sharjah have a tendancy to keep doing things differently from each other, just for the sake of being different, while the Northern Emirates tend to follow Abu Dhabi's lead, because... well, they like the money.
What does this mean? Well, that laws and policies can vary drastically from one city to the next. For example, while Dubai is probably one of the most liberal cities in the Middle East, Sharjah is one of the most conservative. This pamphlet on decency regulations, for example (which most of you have already read, I think), is from Sharjah, and applies very explicitly to Sharjah. In Dubai, for the most part, things wouldn't be all that different than in Canada (although wearing a bikini downtown might be frowned upon :-)
If anyone's interested, I also wrote an essay on Tabnet talking about the comparitive economies of the various emirates and their dependancy on oil revenues (or not, as the case may be). Anyway, I have copied it to my webserver and you can see it here.