As a European I can only tell you what Europe (in general) thinks of the U.S.A.
Mostly Europeans LIKE Americans. We just don't agree with your current government. Most of all your president. How this guy was ever elected will always be a mystery to Europeans. We consider the guy a joke. However, European governments/politicians aren't that perfect either. What to think of a person like Berlusconi?
Also some Europeans feel frustrated that the American culture has such a huge influence on our cultures. Don't forget that Europe is not as unified as the USA. Europe is a collection of countries which all have their own culture and language. Some countries even have 4 official languages. In general, European cultures have far more history behind them than the American culture. So some people feel very protective about their culture. Especially the French who are known chauvinists (stereotyping can be useful sometimes

).
But what really pisses (some) Europeans off about the U.S. is what is being perceived as American Arrogance and being the policeman of the world. For instance, the Bush administration has invaded Iraq by ignoring the United Nations, which was NOT well received in Europe. Especially now it turned out that there are NO weapons of mass destruction found in Iraq whatsoever.
Furthermore, the US Congress adopted a law, making it possible to invade Holland (where the international court of justice is located) in case an American is tried there for war crimes. Holland is an ally of the U.S.A. and a fellow NATO member.
Then there is the question of imposing your will unto Belgium into changing their (stupid certainly, but nonetheless THEIR law) genocide law by threatening to move the NATO headquarters out of Brussels and straight into Poland, where the Warschau pact was signed!
I do not agree with all of the views mentioned above. Although I feel very strongly that the Bush Administration should NOT have ignored the UN and invaded Iraq. However, there are many things I admire about the U.S.A. Especially the way you think and feel about your country. You people are very proud of your country and in my opinion have every right to be.
Often it is overlooked what the U.S.A. has done for the world. When Europe was having a conflict called World War 2 you sent troops to liberate us (only after Pearl Harbor ofcourse

). Even if you are the world police as mentioned above. It is a good thing it is the U.S.A. and not the U.S.S.R.
The world largest companies are American and after WW2 because of the international trade between the U.S. , Japan and Europe the wealth worldwide has increased many times.
The U.S.A. has made plenty of mistakes along the way. Creating a heck of a lot of problems, mostly for yourselves. But still I think it is a great country.