I can only speak from my experience as an American living in Argentina for a little under 10 years, who was a Spanish major in college, and has travelled a fair bit around the continent.
The idea that people in South America "hate the US" has never been my experience. People in the USA on both the right and the left seem to have a paranoid fantasy that everybody everywhere hates Americans. Right wingers think people are jealous of us, while left wingers think we have pissed people off too much because of our abuses of power. I think both of them suffer from the same root problem: the delusion that people everywhere are obsessed with the USA and Americans.
In my travels, people I meet usually see the USA as just another country like any other - they may have a more or less favorable opinion, but Americans are lumped in the same category with Bulgarians and Poles as "foreigners." I've also observed that people are usually smart enough to separate the USA's government from its people. When Bush was in power, people used to sometimes ask me about him, usually in the context of "wow, I really feel sorry for you having a guy like that as your leader." Keep in mind that Bush was extremely unpopular here in Argentina.
I know this may be hard for some Americans to come to terms with, but while there are things that make us a wonderful country, and also some terrible aspects of our past... we are really just like everybody else, and at least in my experience that's just how people here have treated me.
I'm South American (from Uruguay) and there are many more here on HN :)
I'm not representative of my country, and my country is atypical by Latin American standards, but that said, there is quite a bit of animosity against the US, particularly by the old-school leftists (those that were adults during the US-sponsored military dictatorships in the 70s).
The newer generations and the old-school right-wing people bear no such animosity here.
I haven't seen much hatred against the US in Argentina or Brazil either (in Brazil they actually want to measure against and compete against the US in the global stage, not hate them), and there's quite a bit of envy involved.
All Latin American countries consume a lot of US entertainment and media and culture, too.
I'm from Uruguay. Here US is hated by only a few, left ideas oriented people. I think the reason that make US to be hated is because its support to dictatorships and its imperial behavior over almost every country.
But trust me, it is hated by only a few (at least here and the surroundings).