Here's a personal story. Take what you like and leave the rest:
When I was in graduate school I took several classes along with a fellow from Jugoslavia. That is about all I knew about him until my ANG unit was activated to go overseas for the Kosovo conflict. I was not sure whether I would be deployed overseas or at home, so I had asked my professors if I could present my in-class final presentations early. My professor announced in the next class my situation and this fellow turned to me, completely aghast. After that class he explained that he was a Serb, from Belgrade. The next class I gave my presentation, grabbed my things, and left. I remember looking at this fellow and the expression on his face was probably the same as mine. Both of us were thinking 'I can't believe this'.
I reported to my unit, and it turned out that I was assigned to back shop support, so while I was still active, I could still work on campus during evenings. This fellow sought me out to talk war and politics, and I got a glimpse of his family's life under the bombs for 74 very long days. He was very anti-Milosevic but he felt that the U.S. truly did not understand the situation between Serbia and Kosovo, that the US intereference was stunting the internal anti-Milosevic movement (as Milosevic was painting them as traitors) and all was not as black-and-white as it seemed. It was a strange time - going to work each day to work on the jets that were bombing his country, and then coming home from work and looking through emails with pictures and video of the bomb damage in Belgrade.
Afterwards, we became (and remain) very good friends. This fellow still lives and works in the US and he loves it here. Consider that - someone whose family was under US bombing for over 2 months lives in and loves America. He is not a fan of the government, mind you, but he loves US culture and he thinks that our systems are flawed but workable, just as he thinks Serbian systems are flawed and workable.
I could have easily dismissed my friend as a baby-killing Serb and he could have done the same to me by calling me a meddling imperialist pig. But we didn't. We talked. We disagreed on some things, we agreed on other things. We informed each other of our viewpoints. We didn't demonize each other.
I guess the moral of the story is, if you can keep an open mind and see the big picture, it is possible to draw distinctions in situations where it would be natural, almost instinctive, to hate anything and everything about a certain country. I think many (most?) people in other countries can see the difference between America and individual Americans and can keep the opinions of the politics separate from their opinions of the individuals. Speaking as an American, I think we should endeavor to do the same for them.