I'm aware that the OP originally asked about America, but I would like to interject the Canadian perspective.
The very idea of peacekeeping was brought about by former Canadian Prime Minister Lester B. Pearson when he tried to defuse the Suez Crisis. Canada after that point led the world in peacekeeping contributions until recent years when the focus became aligning ourselves with the United States in combat missions, rather than embarking on internationally-supported, UN-approved peacekeeping missions. It was during this period that Canada gained much respect in the world as a neutral, fair, and honest peace broker. Canada played a central role in defusing conflicts around the world. Today, Canada contributes just 200 UN peacekeeping troops.
I believe that America (and Canada and the rest of the developed world) can, and should, play a role in global peacekeeping. First, America should play a role in global peacekeeping because it is the wealthiest nation on Earth (in terms of GDP) and many of the conflicts plaguing the globe are a result of the United States intervening in the first place. But a few things need to happen first:
1. The US currently takes a very anti-internationalist stance. It needs to learn to act with other countries and not unilaterally. Flagrant disregard of international law and opinion does not win you new allies and alienates your current allies.
2. The US military has been involved with some alleged war crimes most recently in Iraq, Afghanistan, and Pakistan. People in developing countries are often mistrustful of American troops. Either the US needs to send troops in the form of UN peacekeepers, or it needs to revise its rules of engagement so that innocent people aren't being obliterated with Predator drones.
3. The US must soften its rhetoric. That does not mean "Do not take sides", but strongly condemning one side over another jeopardizes your ability to broker lasting peace and compromises your neutrality. Canada, a country with extremely similar foreign policy positions to the US, managed to be respected as a neutral peace broker at one time. That did not mean Canada did not take sides, but it meant statements from Canadian officials were measured, calm, accurate, and restrained.
4. The US is accustomed to taking a leading role when international forces are deployed. It does not have to do this. As evidenced by the aerial intervention in Libya, other developed nations are perfectly capable and willing of taking charge. The US can still play a big role, but it doesn't have to act separately and dominate militarily all the time.
5. US intervention comes across as imperialistic at times. Therefore, when US military forces enter another country, it must do so as part of an internationally-sanctioned coalition. Iraq must never be repeated.
Though I'm fully aware that pigs will fly before any of that happens, it's still nice to dream. Canada has a decent shot of reverting back to its old peacekeeping ways, though, simply because we have a history of doing it, and it's a popular sentiment within Canada.
