I think it might be remembered in a similar way that Rome is remembered now.  I think it would be remembered for its demonstration that democracy can exist in a leading nation.  I don't know how many democracies existed at the time America was founded, but from what I understand there were very few, if any.  Most were probably monarchies or some form or aristocratic government rather than true democracies. From that democracy was born a recognition of a set of inalienable rights that protected dissent, self-protection, privacy, and religious practice.  I think that really helped shape the world and continues to do so even into this century.I think that the economic and military power aspects of America would be remembered more as results which flowed from the political structure.  We can point to Napoleon's France or Charles of Spain's empire during the 16th Century as being examples of nations with strong armies, but we don't really talk about any long-lasting effect that they had on the world (as we speak of Rome).  I think that ideas and institutions are more influential in the long term than economic or military feats.