Should America get out?
Well, now here's how I see it:
If the USA does leave, then what will happen? First, violence will decrease, the common enemy is gone, then certain groups will establish 'territory' and begin small wars with each other, and I think quite quickly one group will establish it's dominance over the others and achieve sovereignity over Iraq.
But there's one thing wrong with this hypothesis, it's assuming that other nations stay out of it. Even if the USA gets out and never looks back we still have the Syrians, Turks, Arabians, Al Quadea, European Powers, Russians... All these people will have an agenda with it, now while none of them will go in directly like the Americans did, they will support their favoured group, send weapons and supplies, provide propoganda, provide shelter and training.
Ultimatly I find it quite unpredictable how it will end up, I suspect many will think of Al Quadea will have a strong advantage, but the Iraqi's are used to a secular dictatorship, they probably don't want a theocracy and they're tired of violence. Once the Americans are gone I'm not sure how much support they will be able to get. Many Insurgents in Iraq I suspect will return to simply trying to earn a living, probably a large number will resort to crime due to ruined infrastructure.
I can see the Europeans ending up with another puppet secular dictatorship.
But I don't think that will happen. Even if the USA does pull all it's troops out I think that they will still try to influence the outcome of the ensuing civil war. I think they could very well end up with another USA supported dictatorship.
Which one would end the fighting will lowest casualty count?
The one where America pulls out and then supports a group that swiftly gains control of the rest of Iraq and sets up another secular dictatorship. This time with someone a little more loyal.
What do I think would be best for the world?
What I would really like to see in Iraq, despite the infinitly low probability... Would be a communist revolution, A true communist revolution, unpolluted by western pressures. I think that what this world really needs is a communist nation to succeed.
Ok, so what would happen if the USA doesn't pull out? Well I don't think we will ever see a stable democracy as long as the USA is puppeteering it. I think that even if the USA trains Iraqi guards, sets up voting ballets and even holds several elections... the insurgents will not stop, especially with all the international pressure and support they're getting to continue the fighting. It may last as long as 10 years before being toppled by the insurgents, but It'll turn into another afghanistan/vietnam first.
There is no way I can immagine the Republic surviving without massive human rights violations. And that would be too much of a cover up for the USA, they could pull it off in the cold war, but not today (I hope!).