An Alternate History of the Invasion of Iraq

As I was driving today, I had this rather random thought. How would the course of human history have been altered had the United States not invaded Iraq? 

I am setting aside all the pros and cons of why we invaded. For my question, that isn't a relevant consideration. What prompted this odd inquiry was that prediction by Nostrodamus that there would be a third "Anti-Christ" rise after the fall of Nazi Germany. So the question reframed becomes, "How would leaving Saddam Hussein in power in Iraq have changed history?" Or perhaps, "Might an unchecked Saddam Hussein risen to the heights of madness and power in the world that Adolf Hitler did?" 

Tonight, I just want to raise the question. Sleep calls me and tomorrow is another work day. But tomorrow, I will begin an exploration of this line of reasoning. 

And if you have any thoughts about what kind of timeline world history would have taken, in this alternative history of  our post-9/11 world, please weigh in on the subject. After all, in this kind of pursuit, there can be no wrong answers. Let me hear from you.