Of course the preferred term depends on where you live, however:

American Indian is preferred the most strongly by American Indians themselves, at 49.76% according to the 2000 census. Native American is used more broadly by non-Indian people.

I am quite familiar with other terminology, such as First Nations, First Peoples, and Aboriginal (which are used more frequently in Canada than here).

All of which are good words. People have the right to self-identification. My rule of thumb is: if someone who belongs to the group tells you how they prefer to be identified, respect them by honoring their preferred term.