This is a great question. However, it is much to early to tell how our involvement in Iraq has changed our foreign policy. With a new election on the way, it could change again. In light of all this, I would say that our involvement in Iraq has polarized our country. Let me explain.
There are those who believe it was a huge mistake to enter into Iraq. These people believe that we should not interfere in the world. They believe that we have enough problems in our own country. For these, America should not be an international police force. Stay out is the point. The more radical folks in this camp do not even care if Iran has a nuclear program.
On the other side of the spectrum there are those that want to be more hawkish in our dealings with other nations. So, for instance, nothing if off the table when it comes to Iran and their nuclear program. Will we go in there with force? Possibly. If so, our international politics have not changed much.
In the end, the best answer is that we are more polarized than ever.
The invasion and subsequent occupation of Iraq began a new era both in US Foreign Policy and in how the US conducts wars.
Although it is true that the US has exerted its power throughout the world from the earliest days of the Republic, in most cases we have been reluctant to launch large-scale invasions, particularly outside of the Western Hemisphere (the Monroe Doctrine). Instead, in the post WWII era, we have often fought our wars by proxy, particularly in the Middle East where we used covert operations, like the overthrow of the democratically elected government of Iran, arming the Mujahideen to fight the Soviets in Afghanistan and aiding the Iraqis in their war with Iran. Indeed, we once saw Iraq as a counterweight to post revolution Iran.
On occasion we have intervened with our Armed Forces, but always with extreme reluctance in the post-Vietnam War era, and usually against a foe much smaller than ourselves (Panama, Grenada, Somalia, the former Yugoslavia). With our invasion of Iraq the US signaled its willingness to use military force to exert our will. As noted in the answers above, stated US policy had been against "Nation Building" and indeed, publicly at least, that was not the reason for our invasion of Iraq. However, when no Weapons of Mass Destruction were found, our stated reasons for invading Iraq changed from protecting us from a looming threat to building democracy in the Middle East. Unfortunately, despite the promises of Bush Administration officials, and their neo-con mentors, the reality of Nation Building proved to be much tougher than first imagined and the forces committed proved inadequate for the mission. (This despite the warnings of General Eric Shinseki, who was retired early for voicing his concerns.) This failure in Iraq now calls into question the entire Bush doctrine of preemptive warfare, and once again (as noted above) the world community is wondering just what the current US foreign policy is.
Besides the polarization of the US electorate, another result of the wars in Iraq and Afghanistan will be the need to rebuild the US military. The US had hoped to fight the Iraq war “on the cheap” but it has proven to be anything but. Besides direct operating expenses, there is the untold cost to our soldiers, many suffering form traumatic brain injuries that will only manifest themselves months or even years after combat.
The question here is how long will that process of rebuilding take.
After the Vietnam War the US Military, the Army in particular, went through a long period of self-examination and soul searching, slowly, and at times painfully, for the right path forward. Eventually the Army did rebuild itself into an all-volunteer professional army of the highest standards.
The results of that long nurturing process where on ample display during Operation Desert Storm, and indeed, when US Forces engaged Iraq units during Operation Iraqi Freedom, the outcome almost always lopsided to b=out charitably. (See the Battle of Objective Montgomery for an example of how superior US training won the day even when all the 'breaks' favored the Iraqis.)
There is an old saying: Good swords are kept clean and sharp, but the very best swords are kept in their scabbards.
Our soldiers are a valuable resource that should be used with the greatest of care and only when absolutely necessary. The invasion of Iraq meets neither of those requirements and our military has suffered the consequences.
Some of the adults in my family insist that when George W Bush ran from president the first time he was critical of so called nation building by previous presidents. Examples, would be like the Clinton Administration's (along with NATO) involvement in the Balkan Civil War, and the American involvement in Somalia (like in Black Hawk Down.)
Then after 911, President Bush decided nation building might be a good thing.
But frankly, I don't see how much changed. Lot's of presidents have meddled in other countries, beginning with Thomas Jefferson sending the navy to the Mediterranean to object to the Dey of Algiers taking American ships. Madison and Monroe continued along the same line. Monroe published the Monroe doctrine, which said that the United States would oppose recolonization of countries on the American continents by European countries.
Other presidents (Teddy Roosevelt and Harry Truman) expanded that idea. So maybe not much has changed.