Try reading up on good ol' Colonel Chivington and Andrew Jackson. Please, do this. The Indians were a victim of a genocide.
They're still here, but then, Hitler and Stalin didn't exactly succeed 100% at killing Jews and Kulaks, either.
IMHO, the experience the Indians had would have been a lot better for them had they been able to keep their full 1491 population in dealing with Europeans. Hell, that just gives me an idea for an ASBs thread...
American policy on Indians was schizophrenic. Some (like the above examples) really did push for genocide, but others (notably early missionaries and Americas late 19th century government) pushed for integration. Others (Jefferson being an important example) pushed for separation. Eventually integration became the main policy, after most Indians had already died or been pushed off their land, and the area that really experienced integration was the Northwest and the Great Plains.
Side Note: Jefferson originally felt much of the Louisiana purchase should be set aside for Indians, and that theory would later be used to justify the Indian Territory.