This is a very subjective question - most Americans will undoubtebly say 'yes', but many people around the world will say a resounding 'no'.
Being objective is difficult; there are a lot of great things about America, but there are also a lot of bad things. It's the same for every country in the world - and I'm sure most people would call their own country the 'greatest' country in the world.
In terms of economy, the answer is no; in terms of healthcare the answer is no, in terms of sports, the answer is probably yes, in terms of.....blah blah blah...these are my opinions and you can argue about them until the cows come home.
Perhaps there is no answer, and the question should be more like "Should America strive to be the best country in the world?"