Some argue that we should assume guilt for past actions of our ancestors or culture. In particular for the United States, we are supposed to assume guilt for the conquest of Indian territories and slavery. In addition to guilt, some presume that we benefited from the conquest and slavery and should pay reparations. Let us examine the historical situation to see who, if anyone, should feel guilty.
First, are we responsible for the actions of our ancestors or predecessors in our culture, tribe, or nation? Most existing and past cultures believe that crimes or affronts committed by a member of a family, tribe, or nation either in the present or the past are the responsibility of all living members of that group. This has led to wars and slaughter as acts of retribution. Modern societies, mostly Western, have abandoned this notion, although some individuals and sub-groups still insist on vengeance. So this first question depends on the cultural values of the group making the judgment, there is no world-wide agreement.
Second, in Western cultures, responsibility for an action is generally assumed to depend on whether the accused had a realistic choice or the ability to intervene. Clearly for events in the past we the living have had no choice or ability to intervene. And even in the past, most had neither a realistic choice nor the ability to intervene. However some actively chose or could have intervened in the guilty actions.
Third, what about the details of a presumed bad action? Is there a balance of guilt if all parties contributed to the situation, or if the offended party thought the action was proper except when applied to themselves? In this context was the action consensual? Lets examine the history.
In the 1500's when Europeans first came to the Americas, the world was a seriously hostile place. The Spanish had just freed themselves from Muslim rule after centuries of war. Those that came to the Americas were rough and tumble adventurers just barely, if at all, controlled by the Spanish Catholic Church. Their conquest of the Aztecs, Inca, Maya, and others is often considered a brutal abuse, and indeed is was brutal. However the indigenous peoples had the same view of conquest as the Spanish, they had been conquering and enslaving their neighbors for centuries (which is why the Spanish had many indigenous allies). Had conditions been reversed, these peoples would have happily slaughtered the Spanish. So clearly neither the Spanish nor the indigenous peoples were the nice neighbors we would wish to have today, and there is little reason for any living person to be held accountable.
Later in the 1600s, the world order had changed little. As Europeans reached the East Coast of North America, they were a varied bunch. Settlers to the North East were mainly entire communities and families, and those to Virginia were commercial adventurers and disinherited minor aristocracy. These people were English, they thought of themselves as English and they acted like English, but for the most part they didn't think of themselves as conquerors, they settled where no Indians had claims. The French to the North and the English in Virginia were founding aristocratic communities with lords and peasants. Families settling in the North East were mostly English families fleeing persecution by the Church of England. They established communities as tiny theocracies. The America of the Declaration had not been discovered yet. The Indians operated in the world-wide mode of the time, conquest or negotiation with neighbors as strength and necessity dictated. So both groups agreed that conquest and retribution were natural (unless it was against themselves).
Once established, the advantages of the Europeans, including technology and food and necessity production, allowed significant increase of the European populations. There began the inevitable conflict. The Indians had limited food and necessity production, and relied on large territorial claims for hunting and gathering. And there were trouble makers in both communities. In any large conflict, the advantage was with the Europeans, although many died on both sides.
In the 1700s, the world order was still pretty much unchanged. In North America, the conflicts were larger and more organized. The French, British, and Indians, and later the Revolutionary Americans, fought, negotiated, made treaties, juggling for authority and territory. The Indians chose and changed sides just as did the Europeans as necessity and advantage seemed to dictate. They all still subscribed to the need for conquest and retribution. Those inclined to peaceful relations never seemed to maintain control. So no moral high ground here for anyone.
In the 1800's the tide turned against the Indians. The Louisiana Purchase and the War of 1812 pretty much settled the European claims in America. The British claimed Canada and the North West, the Spanish the South West and Mexico. New American immigrants pressed across the Appalachians and into the deep South. They were a rough bunch, used to centuries of war in Europe. The world-wide order was still conquest and retribution, but now the Indians were not equal players. They were forced westward and onto reservations, and relieved of land in questionable deals. The peaceable Indians and family settlers were caught in the middle. There was a moment of hope mid-century when families migrating to the West and the Indians along the route operated together in normal commercial relationships, as Indians provided ferry crossings and sold food. But the Indians awakening to their loss of prominence, and bad behavior on both sides killed the hope. By the end of the century the Indians were conquered peoples.
In the 1900's the Indian population melted into the general population or languished on reservations. In the later half of the century, some tribes reasserted sovereignty over tribal or reservation lands, but many still remained wards of the state.
So where do we stand now? For many, by the first question above, we are guilty simply because some of us in the past used force and conquered. There is no point in arguing with such people because they do not recognize principles two and three (choice, ability, balance of responsibility), and they do not acknowledge progress in society, which necessarily implies improvement from prior behavior. But by principles two and three it is clear that we the living had no choice or ability to change the past, and that in the past the "victims" were at least equally responsible for events, and had the result been opposite would have argued that they were blameless.