Which American continent?
In the South American continent, Central America, and Caribbean, the Spanish/ Portuguese colonized those areas mostly for trade (gold, silver, slaves, etc.). In the case of North America, the American colony was founded for freedom of religion, but later taken control of by the British Crown. So the original intention of the European settlers was to have religious freedom, but the Crown had other ideas, mainly to expand their empire and trade. Likewise, the French and Spanish used their territories in North America (France with Acadia [before it was taken by Britain in the French-Indian War aka Seven Year's War] and Louisiana Territory, Spanish with Florida) for Trade. So that's basically saying, the settlers wanted freedom, while the monarchies all wanted to expand their empire and trade commodities that were not common in Europe, like the beaver pelts that came out of Acadia.
Long-winded answer I know, but I hope this gives you some info nonetheless.
