Certainly one can choose to ignore the past, or to develop a sense of historical context, such as the previous answer aptly does. Any discussion of forgetting or ignoring the past, however, requires reference to the oft-quoted Spanish philosopher and writer George Santaya: "Those who cannot remember the past are condemned to repeat it."
Santayana was referring, of course, to the propensity of people to fail to learn from the past. Without recourse to history, it is difficult to learn how to move forward as a society. The United States has dark chapters of its history -- most notably slavery and the continuation of racist practices well after the Civil War -- but most Americans recognize that the country has learned from that period of its history in a way that has helped it to avoid similar mistakes. In the case of colonialism, history remains a powerful motivating force in many cultures. European-imposed legal systems and social or cultural practices not attuned to the indigenous social and cultural practices left enduring scars that have taken time to heal.
There are instances throughout history and across the world where forgetting or disregarding the past could prove helpful. After the September 11, 2001, terrorist attacks on the United States, then-President George W. Bush stated, "This is a new kind of -- a new kind of evil. And we understand. And the American people are beginning to understand. This crusade, this war on terrorism is going to take a while."
President Bush's use of the word "crusade," in that context, however innocently intended, became a lightening rod for many Muslims, for whom "crusade" conjures images of European wars waged against Islam -- wars waged during the Middle Ages. Ideally, the president would not have used that word; that it resonated throughout the Islamic world in a negative way was in indication of how deeply history has affected contemporary thought.
This is, of course, a question to which there can be no objectively correct answer. Answers depend largely on the opinion of the individual giving the answer. My own view is that what has been done in the past is less important than what is being done in the present.
My father is a native of the Philippines who is now an American citizen. I have been an American citizen all my life. I am well aware of the fact that the United States colonized the Philippines and that it treated Filipinos very brutally during the process of taking the country. However, I do not feel that this is very important given that it was done over 100 years ago in what might as well have been a different world.
What I think is much more important is how the United States treats the Philippines today and how it treats Americans of Filipino descent. In both of these areas, there is nothing really to complain about. Therefore, I have no reason to remember the past in the sense of still being angry about it. Since my country treats me, people like me, and my ancestral country well today, I do not think it is important to dwell on the fact that the US treated my ancestors badly.