In the five hundred years between Columbus and Wounded Knee, tens of millions of native peoples died from disease and conflict with European explorers and settlers. There can be no doubt that this was a genocide on every level: socially, culturally and linguistically.
In the smaller, specific context of Wounded Knee, this too was a genocide. It involved the massacre of 150 - 300 men, women and children for who they were and where they lived. It was senseless, brutal, racist and quite simply, murder. Most historians agree that the slaughter of Native Americans at the hands of the U.S. government in the 19th century is one of the darker stains on our national history.
The United States has a history of helping to rebuild countries it has been involved in destroying during wartime...except the Native Peoples of America. To this day we are still trying to take away what is rightly theirs and not following through on promises made in treaties.
People in the United States shy away from the word genocide, especially if it involves them. The killing of millions of first nation individuals should be and is considered genocide. We don't teach our children this, therefore it is a topic that is left to discover ourselves. Many Europeans brought over diseases that wiped out entire populations of first nation people, including small pox. If you are interested in this, a book called Lies My Teacher Told me has a great chapter inside called "The Truth about the First Thanksgiving" and it talks about how Europeans have created genocide against many of the first nations people.