1. Do you think America are the World's Policemen
Yes, and we have been ever since the Second World War. Following the end of the war, most of the rest of the world's nations were weak enough that the threat of U.S. intervention (or, in cases such as Korea, the act of intervention) was perceived as the only barrier to being overtaken by the Soviet Union. The leadership of Western European nations in particular were fearful of falling to the same fate as much of Eastern Europe had at the time. Due to this, and due to the fact that the U.S. spearheaded the United Nations and had a personal stake in making it into a credible governmental body, we sort of slipped into the role.

2. Do you think America should be the World's Policemen, if so/not, why
The need certainly existed during the Cold War. After the fall of the Warsaw Pact, the need has become more debatable. Personally, I don't know what would happen if the U.S. retreated from that role, but the only thing I can readily think of is resuming the isolationist policy adapted between the First and Second World Wars, and IMHO that should be avoided. Quite simply, we've meshed outselves way too far into the global scene to be able to pull out without doing a lot of damage. While the world is more stable today than it was during the 1920's and especially during the Depression years, I still can't help but return to looking at that model as an example of the potential consequences of an isolationism policy on the part of the U.S.

So, in essence, yes. If we weren't currently in the position, I'm not sure what I'd think about the idea of the U.S. assuming the job, but we've taken the job and shouldn't leave now.

3. How would this idea seem to the rest of the world that is being 'policed', eg Europe or the Middle East
Due to the communist threat mentioned above, best I can tell, Europe welcomed the U.S. during the Cold War. But, now that the Cold War has been over for more than 10 years, it looks like Europeans are beginning to resent the U.S. influence in their lives. The Middle East, except for Israel, certainly doesn't want us there...but (and I think I'm in the minority on this board) I think we're doing the right thing helping to keep Israel secure.

BTW, some minor things may not be 100% accurate; I typed this up off the top of my head...but the basic concepts are my interpretation of recent history, and I'm sticking to it.