So, Qaddafi apparently has lost in his effort to retake the major oil head and refinery at Brega against the rebels against his regime, meaning that they control about 80% of Libya's oil, with the refinery particularly crucial according to the generally reliable Juan Cole at http://www.juancole.com . Needless to say, the uncertainties about oil supplies, particularly since the uprising in Libya began, have helped push up the price of oil, past $100 per barrel on both West Texas Intermediate and the roughly $13 more expensive Brent crude, which is the price most of the world outside the US pays (this gap an oddity only around since December), although the general trend with the world economy growing while world oil production has not risen at all for the last half decade is clearly going to be for prices to rise over the foreseeable future, even if there is a downward correction when these uprisings settle down.
While Libya is a major oil exporter, and fellow OPEC member Bahrain continues to have major demonstrations by the Shi'i majority against the Sunni monarchy, it continues to be the case that generally major oil exporting Arab nations are having fewer and less severe uprisings than non-oil exporters. The main latter ones without uprisings continue to be Morocco and Syria, both of which have had some minor demonstrations, but apparently remain largely calm.
However, some other major oil exporters have either experienced demonstrations or are very nervous about the possibility of there being some. Much attention has focused on the big one, Saudi Arabia, where Shi'a are about 17% of the population and concentrated in the oil producing Eastern Province and have long been oppressed by the Sunni majority. There have been calls for reforms, although no demos yet. King Abdullah has responded with a $36 billion plan to spread around a bunch more money. Key blog on the Kingdom is John Burgess's Crossroads Arabia at http://xrdarabia.org . According to his links, probably Abdullah's move will work, and the majority Sunni population remains largely loyal to the royal family.
Another less-publicized but somewhat similar situation has arisen in the United Arab Emirates. There the problems are more with expatriate workers (as in Kuwait also), who make up a substantial portion of the labor force. The UAE rulers, who also have a lot of money, at least in Abu Dhabi (Dubai is banrkupt and kept afloat by the Abu Dhabi folks), are imitating the Saudis and have announced a major money handout. One can follow events there through John Chilton's The Emirates Economist blog at http://emirateseconomist.blogspot.com .
Finally, the latest Arab oil exporter to have demonstrations, fairly serious actually, has been Oman at the southeast corner of the Arabian peninsula. Unlike the previous two cases, they do not have nearly as much oil or money, but the traditions there have also been to be much more tolerant of dissnt. Part of the issue there is regional, with most of the unhappiness in the western areas of Dhofar near Yemen (which continues to be perhaps second to Libya in terms of the seriousness of its current uprising), an area much poorer than Muscat in the east where the oil is. There is a potential for greater trouble, as Dhofar rose up in the 1980s militarily and could do so again. However, the Omanis belong to the Ibadi sect of Islam that is neither Sunni nor Shi'i. having split off even prior to the division between those two. The Ibadis seem to be more tolerant and easy-going, in contrast to their more hardline Sunni neighbors (although in Yemen part of the issue is dominant Sunnis against rebellious Zaydi Shi'is in the northern mountains), and ruling Sultan Qaboos seems to be making conciliatory moves towards the demonstraters. One can follow events in Oman at Dhofari Gucci's blog at http://dhofarigucci.blogspot.com .