The Lesson of Iraq (1958)
theatlantic.com
theatlantic.com
Gulf states would switch to a financial economy as quick as possible, states such as the UAE and Qatar would succeed but states such as KSA and Bahrain would fail. In the immediate short term nothing would happen but within a year there would be widescale protests through out KSA as public sector employs realise they have no equity what so ever.
Outside of the gulf, North African countries would undergo massive social upheaval as the ruling elite and powerclass fled and left behind those who are unforunate enough to not be able to escape. The Levant would be sheltered primarily due to their lack of reliance on petrochemical dollars though Syria would degenerate.
Iran would diversify and overcome the situation. They've been under embargo one way or another for nearly 30 years so they have experience in maintaing the necessary cash flow to pay their citizens and avoid major economic collapse.
In the medium term you would see the complete collapse within the gulf of the ruling class. The royal families would flee and take as much money as they could while their underlings would be handed the reigns. They would fail and social anarchy would take over before the common people reverted back to Islamic governance. For a generation at least you would see fundamentalist Islamic theocracies pop up as people vied for power but no real governing institution would rule.
Now that we're looking so far into the crystal ball things could go either way but there is a possibility that the Arabs would return to a Kilafa style of governance which would actually reunite the Arab World, see human rights (at least an Islamic interpretation of it) flourish, education take off, economic and social reform at a level never thought possible etc etc.
But really, at the end of the day shutting the oil off will probably only have minor consquences. The Middle East has spent trillions of dollars diversifying to protect themselves from the inevitable reduction in demand for oil.
Iran is quite an industrialised and high-tech nation with many skilled engineers. I know they look a bit bad when they release videos of model aircraft as fancy stealth bomber. But I have no doubt that they'd overcome such a situation.
It looks much worse for the Arab oil nations because they lack industry, skilled engineers or labour, or any kind of research. The financial market is a fragile thing and well Dubai is build on sand. We've seen in the crisis that nations with an industrialized base did much better than nations who were more focused on financial markets.
In Arab oil countries the situation is that large projects are designed by European, American, or East Asian engineers and architects and the construction is done by basically South Asian slave labour. In the end the building is left but nothing of the know how and skills that came with the project.
Another big indicator is the lack of a Saudi space program. Usually if a nation just has too much money a space program is a great way to boost engineering, science, industry in the country. Even Nigeria has a space program. Alternative would be a build up of the military. Which the Gulf states are clearly doing. But they import all their weapons from Europe or the US. Again no domestic research or industry. And military isn't really an investment. Once you try to reduce the budget the fighting power decreases dramatically and your past investments start to rot.
edit: My crystal ball is therefore rather showing negative picture. I believe there will be huge social unrest. It won't happen immediately but gradually. It will turn out similar to Egypt, Libya, or Syria. Currently the Saudis and Gulf states are using radical Sunni Islamists as a way to fight Shia Islam/Iran. They already used Islamism as a tool against Panarab Socialism but their current support goes far beyond that. And this will all eventually come back to them. There could even be an open war between Iran and the Gulf States.
I could go into detail if you would like but its a very complex and painful story. The wikipedia page probably covers it rather well.
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Democracy isn't magic and just suggesting that we should help democratic parties when we can is a 'no kidding' suggestion.