It all depends on what your definition of "in progress" is.
Just because something is not in full swing, that doesn't mean it's not happening.
Technically WWII is often agreed to have started when Germany invaded Poland. But this can be argued, because it wasn't a "world war" just because of an invasion. However I agree with the majority of historians here. But...you could go even further back to the root of it - the end of WWI and the Great Depression.
So in my opinion, WWIII has been in progress since the first Gulf War. This is because the US put bases in Saudi Arabia and pissed off bin laden. Then 9/11 happens...and we've been in the real war ever since. It's only going to get worse from here. That is what WWIII is all about. So yeah, woohoo, execute Saddam. Big deal. What are we going to use his corpse as a shield from future terror attacks and who knows what else will be coming in the future?
A nuclear Iran is inevitable at this point. And when you consider that the Iraq war has done nothing but make more enemies of the US, it only looks like there is a whole new generation of terrorists on the way...and these will have nuclear capabilities.
And let's just consider Russia and China - they have an oppurtunity to take out the US through the surrogate of supporting th rogue nations, even if it's completely under the table and out of sight. Surely I think they would take the chance.
It's all coming together.