An interactive map from The Economist lets you click on member-states of the Arab League for relative scores on democracy, corruption, and press freedom, as well as overall stability:
You know what country looks pretty damn shaky? Iraq. Odd, what with our having bombed them into the age of liberal pluralism just eight years ago... Syria is similarly close to head of the line on the instability index, though most indications are that the government there would have no compuntion about brutally dispatching the opposition at the slightest whiff of unrest. Then again, the same could be (could have been) said for Qaddafi in Libya. And while the Gulf oil states mostly look pretty quiet for now (Bahrain excepted), no one's holding the reins on this tiger.
For what it's worth, here's an interesting take on what the future of the House of Saud may look like.