From an economic standpoint, the 1990s was the time in which the US entered the Globalization phase by approving the North American Free Trade Agreement (NAFTA). When the world's largest economy validated this economic approach, it changed international business and nation states, probably permanently, and not necessarily for the better.
Add to this our pioneering efforts in the development of the internet, and an additional economic engine/revolution was added to global business and trade.
I would have to agree that we put ourselves into the role of world police or big brother. We took it upon ourselves to help protect undeveloped countries of the world from aggressors.
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.
After 1990, it really appeared that the United States would play the dominant role in the emerging global economy. At that point in time, the Cold War had ended and the United States had no serious competitors for global influence politically or economically.
Because of this, it looked as if the world would follow the lead of the US. A good example of that seemed to be visible in what happened after Iraq invaded Kuwait in 1990. The first President Bush managed to get a huge coalition, backed by the UN, to sanction an invasion of Kuwait. This would have been unthinkable during the Cold War.