The BBC's Washington correspondent Justin Webb has been investigating anti-Americanism in a three-part series for the BBC News website and BBC Radio 4.
Here, he answers some of your questions.
Why do many people want the USA to be the world's policeman, yet when it does intervene in another country's affairs it is accused of imperialism?
Stephen Brown, Belfast, Northern Ireland
I agree with the thrust of this question - that the US is looked to for political and physical aid but then attacked for providing it.
Often as well the US is doing what other nations would like to, but simply cannot.
After all, you could argue one reason the US is so dominant is the failure of Europe to be as successful on the world stage, through self-destruction in two world wars and through self-induced economic stagnation in much of the period since then.
This is not the fault of the US.
Given that the US is responsible for so many deaths in Iraq and Afghanistan, isn't it understandable that so many ordinary people despise the US?
Adam Cooper, UK
I suppose it is understandable, and it is not my intention to suggest that US activities should never lead foreigners to despise the actions of specific US administrations.
What I wonder is whether the same standards are used when comparing US actions with those of others.
Take the case of civilian deaths. There is no doubt that US actions have caused many, many civilians to die in Iraq and Afghanistan.
I also think is fair to say that there is a strange reluctance among many Americans to face up to this fact - it is not mentioned much on the media here.
But the US does not kill civilians as a matter of policy. Others, including of course some Islamic radicals, do.
As an American living in France, your piece caught my eye. Could you please explain more about what you mean when you say there's an "intense dislike of what America is - not what it does"?
Carih Branson Braud, St Contest, France
I think I should have said "not just what it does". In other words there is obviously a dislike of some of the policies of the Bush administration but the point I make is that anti-Americanism runs deeper, goes to the question of whether the nation is exceptional and worthy of special status or the opposite.
Many Europeans in their heart of hearts believe the opposite - that America is a dowdy dull-witted place which adds nothing to high culture or the real well-being of mankind.
That's what I mean by a dislike of what America is.
I personally find overt criticism of the USA to be unfair. Do you think a lot of it is borne out of jealousy?
Peter Walsh, Winton, New Zealand
Human beings do not always react well to being forced to confront their own inadequacies, do they?
I think foreigners are sometime perplexed by the relative success - particularly economic success - of the US and like to believe that it has come by accident.
The US is in many ways terribly flawed but, yes, the outside world is sometimes unwilling to give credit for the things that are done well here.
Does a sense of inferiority, or superiority, play a part in French anti-Americanism?
Paul, Charleston, South Carolina, USA
Oh, you bet! Actually both as you suggest.
We were told by several thoughtful French people that France never got over its sense of outrage that the US managed to create a republic from scratch and soon didn't need the help of France.
And yet at the same time there is this strand of thought that suggests that the US contribution to the culture of the world is limited to hamburgers and films with happy endings.
So America is resented for its success and yet its achievements are deprecated all at the same time!
In many ways I represent all of the things Europeans seem to hate about America. I am from Texas, a gun owner and NRA member, and I voted for George Bush twice. My question for Mr Webb is, given all he said, what does he suggest we as Americans do to help our reputation overseas?
John, Irving, Texas, USA
To be honest I think there are many people who simply are not reachable.
They have decided that the US is a force for bad and they use things like gun ownership to back up pre-existing prejudices.
But all is not lost. The US academic Julia Sweig sets out a very reasonable programme of actions and approaches in her recent book Friendly Fire.
The US needs to keep its nerve I think, to react in a proportionate way to the wrongs done to it, and never forget that most outsiders are really not in the hate brigade, not in Europe, not in Venezuela, and not even in the Middle East.
You do not have to give up your Texas lifestyle but you do need to accept that other lifestyles might be equally valid and worthwhile.
Sometimes it comes down to a matter of tone, nothing more. It's about how America talks with the outside world.
The trouble with the anti-Americanism label is that it is attached to anyone who makes negative remarks about American foreign policy. Why is it never applied when strong criticism is levelled at other countries? In the West there is consistent criticism of China, Russia, and Iran without ever being dismissed as anti-Chinese or anti-Iranian. Why is that?
Inge Solberg, Oslo, Norway
This is a fascinating question and several interviewees suggested to us that Americans were peculiarly sensitive, even infantile, in their desire to be loved.
Is it perhaps that they seek legitimacy in a way that other nations simply do not bother?
China, Russia and Iran are good examples of nations that pursue their self-interest with little or no concern at all about the human cost.
The US represents, I suppose, a set of ideas about human conduct which makes approval or disapproval of its behaviour much more important to Americans.
The US has by far the biggest and most widely deployed arsenal of nuclear weapons directed at a huge number of human targets in many nations. Why should these weapons not be a focus of anti-war and pro-peace protests?
Joe Bridy, Philadelphia, PA, USA
I suppose my point is that the peace campaigners tend (not always I admit but often) to focus on the US rather than on the weapons of mass destruction held by other nations.
China for instance has just tested a weapon in space. Where were the street protests?