Well, while I'm European, I can't say I speak for Europeans; I have no special knowledge. Take this with a big grain of salt.
You know the Elder Race trope in sci-fi? I think we Europeans think of ourselves a bit like that. Having suffered so much in both world wars, and having since mostly stopped fighting, we see ourselves as mature. Between the 50s-80s, we also mostly embraced a style of social-democracy with strong safety nets, which made us think of ourselves as compassionate. And our ancient heritage - cities, traditions, etc - make us feel wise.
Americans are seen a bit like the ancient Greeks and Romans saw the Barbarians. We might like some of you (hell, some barbarians were made into Roman emperors!), but you are still seen as violent and dangerous; be that due to your foreign policy (Vietnam, the Balkans, Iraq) or your way of life (love of guns, poor social safety net, anti-science beliefs, etc).
But the real problem is that you are powerful, and you use that power. The previous poster might be incorrect regarding that particular policy, but their misconception comes from the fact that the US has been forcing IP treaties (e.g. ACTA) on other countries. And it's not just those treaties, it's your products and even your culture. You mentioned Coca-Cola. You know how that used to be called in my country, especially during the more left-wing days of the late 70s? The "dirty water of imperialism". The fear of being Americanized exists - and it's not unreasonable.
But you should also know that the US is not seen as the source of all evils, that's probably just what reaches you. There's plenty of internal strife. In my country, during the crisis, the enemies were Merkel and Schaeuble, for example.