Spain: The spainish were the first European power to interact with native american populations. When they arrived in the new world, they began they found amazing new trade items which they began growing in bulk. To make sure they had the labor pool they needed, they enslaved the native peoples of the carribbean, working them to death, then replacing them with Africans eventually. Most of the islands of the carribbean were totally depopulated of natives by the year 1550. Spain also made a point of seeking riches from the larger empires in the interior of South America, destroying both the Aztec and Inca utterly. Spain's ruthless policies were the subject of much debate amongst the missionaries and church officials that ministered to the natives, eventually being brought up at the Vatican for debate.
France: France never really attempted to settle the lands of New France as extensivly as Spain, England or America, and therefore had a much better relationship with the natives in their area. Instead, the engadged in trading, partnering with the natives instead of enslaving or killing them. French trappers would strengthen these bonds through marriage and language. French missionaries did try to convert some of the Huron, but not extensively, fearing forced conversion would disrupt business dealings. This partnership would pay off during the French and Indian war, which, althought the French lost, showed the benefit of treat the indians well.
England - The land-hungry English were constantly at odds with the Indians of the colonies. England's political and religious situation made colonizing very appealing, and as the settlers streamed west the natives pushed back. King Phillips War and the Pequot War are both examples of the types of fighting that continually fouled the English/Native relation. After the French and Indian War however, the English line changed. Not wanting to have to fight another costly war with the powerful tribes of the Ohio River Valley, the English began preventing American colonial expansion. The Proclaimation of 1763 was one such law that indians applauded and american colonist loathed. The English stance on expansion helped cause the eventual revolution, where many tribes joined the British because of their fears regarding American expansion.
Americans - After independence, the unspoken policy of the American government towards natives was "force them to move or kill them." Fronteir settlers, who had no love for the natives who raided and fought back against the westward movement of the Americans, were never discouraged by their government from treating natives inhumanly. Some presidents tried to sign treaties, most of which were ignored by later generations of statesmen. Some encouraged indians to "adopt white customs" hoping that they could be assimilated. The Cherokee, Chickasaw and other southern tribes in Georgia did so, modernizing in the hopes that they would be left alone, which for a time seemed to happen.Then Andrew Jackson, hoping to score points with southern whites who were hungry for Cherokee lands, forced them out in an episode known as the Trail or Tears. From this point on, American policy towards indians was one of conversion and forced confinment onto reservation, a policy which was deeply flawed and never truely managed effectively. Some tribes fought back, such as the Apache and the Sioux, but most were eventually wiped out or forced onto crowded reservations.