I think "great" is a subjective word. What makes a country great to someone else might make it awful to me, if the other person and I don't share the same values or beliefs.
For me, I'd believe a country was great if its citizens had civil freedom, religious freedom (to believe any religion they wanted or no religion at all with no punishment, either from the government or from society), well all freedoms really, not just civil and religious. I'd think a country was great if its government was small and only intervened in day-to-day life when absolutely necessary. If its laws were made strictly for the good of the people. If it prevented wars instead of participating in them. If people of all creeds and colors and backgrounds were held as equal in it. If a primary concern of the citizens and government was education for the children of that country.
This is really far off from what other people consider "great." I've had discussions with lots of folks who think that a strong army makes a great country, or that if a country is rich then it is great, that sort of thing. They have valid points too, don't get me wrong, but their values of "great" and my values of "great" are just different.
No country could fulfill every aspect of what I consider great, it's just not realistic. I understand that. A country can't always help it if it goes to war, for example. If you get invaded, what are you supposed to do, sit on your thumbs? Or stand up for yourself? (As an example.) But I'm a bit disappointed in America. Not America's fault, really. As a child I was taught (mostly by family) that America was the greatest country, the richest country, the freest country (side rant spoiler)
I was told in fact that America was the ONLY free country, because we won all the wars! I still very often hear things like soldier worship because "without a strong army we wouldn't even be free," which I personally disagree with. Without an army (that is, militia) we wouldn't have been free during the revolutionary war, but not so much today. I respect soldiers because they have a hard job and must live away from their families for months at a time and have a fairly high risk of death and are willing to sacrifice for the country, but I do not worship soldiers. They knew all those risks when they went into the military. Other countries are decently free without wars, why can't we be?
Anyways, I was taught from my extremely patriotic family that America was basically the closest thing to utopia and all the other countries were less-than, for various reasons. That America was the back-to-back world war champions, so we could dominate anyone in a war situation. (Even our national anthem is glamorizing war, for goodness sake!) That America was the only place where a poor person could pull themselves up by their bootstraps and become rich, even to the point that poor people choose to be so because there are just endless opportunities here. That other countries aren't even free.
So when I grew up a bit and realized that a lot of this wasn't true, it was disillusioning, disheartening, and a bit disappointing. If I had grown up with a realistic view of America instead of a fairy-tale view of America, I would probably like America much more today, because I would not have been so disappointed.
Anyways. Apparently the USA is ranked 7th in an index for human freedom (
http://www.fraserinstitute.org/research-news/news/display.aspx?id=19171) and 10th in economic freedom (
http://www.heritage.org/index/ranking) which for my my values, places America overall at 7th "greatest" if we disregard wars.
If we do not disregard wars and look at peaceful countries, America is not doing so good. (
http://www.buzzfeed.com/keenan/the-most-peaceful-countries-in-the-world) but just how good it's not doing varies from source to source. Wiki has America listed at number 29, which is a great deal higher than this buzzfeed source.
Anyways! No, America is not the greatest. But it's also not the worst, and we may as well make the best of it and try to improve it for future generations.