Rod Dreher has a posting discussing just this question:
It seemed to me then that I loved America in part because it stands for an astonishing experiment in the dismal history of mankind: an attempt, mostly successful, by people to live in liberty, and to govern themselves. …
All of that is why I love America. But that is not the main reason I love America. The main reason is simple — so simple that I didn’t realize it until 9/11.
I love America because she is mine.
This is my own first inclination as well, but it reminded me of something Lincoln said in his eulogy on Henry Clay:
He loved his country partly because it was his own country, but mostly because it was a free country; and he burned with a zeal for its advancement, prosperity and glory, because he saw in such, the advancement, prosperity and glory, of human liberty, human right and human nature. He desired the prosperity of his countrymen partly because they were his countrymen, but chiefly to show to the world that freemen could be prosperous.
Obviously, this contrast isn’t as consequential as it might seem; in America, there isn’t as much of a difference between the nation or people (“because it was his own country”) and the state or the regime (“because it was a free country”) as there is in, say, France or Germany or Russia. In fact, in a sense, the American nation and the American state are one and the same thing. Nevertheless, the difference in emphasis is a way of explaining many political fissures, especially among conservatives: Wilsonian vs. Jacksonian foreign policy; high immigration vs. low immigration; neo vs. paleo; etc.