History will continue to paint that role in the global community as the 1990s went underway. In addition to the answer above, I think the biggest role became being the world's police.
We find ourselves hearing about Iraq more than anything because it was what George W. Bush chose to do based on the information he had at the time in the 2000s. However, prior to that, Clinton was relied on to work peace talks all over the Middle East. Some progress was made, but that was slow and solutions were never met. Now, we still hunt for terrorists in Afganistan, but our troops are really all over the globe in various policing roles. I have spent time in Haiti, and well before the earthquake, our troops were there because the government is instable.
We are often considered the world's only remaining superpower after the Cold War subsided, but we certainly do not have the financial stability to back up such a claim anymore.
I think traditionally, Americans have been freedom-lovers with an increasing goal of achieving human rights across the globe. The upcoming elections will go to great lengths to demonstrate if we can take care of business at home to continue to maintain our role(s) abroad.