I've often thought that the United States will be remembered similarly to the Roman Empire as a few others have mentioned. Great in some ways, shameful and terrible in others. Such is the nature of power.
Those who have downplayed the US's impact on the world and history due to the length of its existence are not taking into account that the modern world and the ancient world are extremely different with regards to the progress of civilization. Take a look at the difference between the early 20th and 21st centuries (computers, the internet, and nuclear power being the first of many examples that come to mind) and compare the difference to that of, say, the first and second centuries CE, and you'll realize that a straight comparison doesn't make any sense at all. The US's role as a hegemonic power in this day and age in the world, and not just the Western one, is an unparalleled feat, and has had an undeniably profound impact both culturally and politically.
Though neither originated in the United States, it will likely be remembered for being the key influence in the spread of democracy and capitalism through its victory in the Cold War.
It will be remembered for introducing the nuclear age, forever changing the nature of diplomacy and military power, and it will be remembered for the information age through the internet, which was born here through ARPA and grew to maturity in Harvard, MIT, and other universities across the country.
Anyone can say what they like about American culture, but no other culture today has exerted as much of a globalizing force as have the American media and capitalistic consumerism. McDonalds, Coca Cola, Hollywood, Microsoft, these companies have not just exported products but lifestyles, and while the emphasis on materialism and quantity over quality are surely troubling outlooks, they have also contributed, in their own way, to stronger relations between nations out of the growing mutual dependence on trade and profit.
In the end, and this may very well be my own bias as an American who sincerely loves his country for all its tragic missteps through history, I believe it will be remembered more for the good than for the bad, if for nothing else, because history is often written from the perspective of those in power, and though the US's power is in decline and global sentiment is turning against it, it has already left its mark on cultures and history books around the world. Rome was unfortunate in that Christianity would evolve to be the true force that would emerge from its ashes, and Christian tradition does not paint ancient Rome in a good light (with good reason). Though much of Rome's legacy was indeed filled with vice and arrogance, I don't think Rome would ever have been judged objectively given the influence of the Church that succeeded it. While I don't believe in the "good intentions" of the United States, or, frankly, of any country beyond caring for its own self-interests, I do believe that, given the massive power it has wielded in its time, it could have been far worse. A look at the many only recently declassified documents of what went on within the Soviet Union can provide a sobering view on what the world could have ended up like.