It was a poor decision to go in to begin with, staying doesn't fix anything. The area is not more stable than it was when we invaded, it may actually be worse. There was no purpose in being there at any point and certainly no purpose in continuing to stay.
The United States did the right thing to leave Iraq because it is not the United States job or responsibility to instill democracy in Iraq. The U.S. should not try and police the world because it is an impossible and costly task. We entered the country, destroyed our enemies that attacked us, and left the country in what I consider to be a successful military operation.
The United States shouldn't have gotten involved in Iraq in the first place in 2003. However, U.S. forces shouldn't stay there any longer than is necessary as the Iraqi people are responsible for their own sovereignty and security. It's nice that Iraq is free of Saddam Hussein, but at what cost? It's time to bring the troops home and keep them home.
I don't think the U.S. should have gone to Iraq in the first place, but once we were there we should have accomplished the task and left. We were there too long as it was and many Americans and Iraqis died as a result. Wars must have a definable set of goals.
I do not believe the United States should have stayed in Iraq. I think Iraq is progressing fine without us and that is a good thing when considering the deficit within the United States. We shouldn't have to stay there. We did remove the regimen in control and we handed that power back. Job complete.