Rather than say "indians," most people find it polite and politically correct to refer to the older human inhabitants of North America as NativeAmericans.

The more archaic and derogatorily connotated (from the 1800s, from whence come all the cowboys vs indians stories) "Indians" originally derives from the quickly debunked notion that North America was in fact India. Silly fifteenth and sixteenth century explorers! :)

See also "West India" and "East India".
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First Nations, aboriginal, or indigenous people also are ways to talk about this.
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Of course, they are 'native' only in the sense that they were already here when the Renaissance Europeans arrived.  They migrated here from Asia at various times during the last Ice Age.  

''In that sense, nobody is really 'native' of nearly anywhere on earth.  As the north american 'natives' have been there on the order of 30,000 years, the ratio is roughly 100:1 with the time europeans have been there.  Which is the point.''

Not all the inhabitants of that 30K years are the same ancestry as the ones who met the colonists on the East Coast.  Kennewick Man appears to be of a different ethnicity, making it possible that the last wave was the only one related to the current Native American peoples.

Also, while there is definite cause to feel that the Europeans did wrong in many of their dealings with the locals as they expanded the colonies, how long does ones' family need to live in an area to be considered native?  There may well be Europeans with 400 years of history on this continent, putting them at only a 20:1 ratio.  

''That is an age-old question, but probably not one with an answer, useful or otherwise.  On the other hand, one must be careful not to use this as a cover.  There is some truth to the 'history is full of these sort of abuses' stance, but it doesn't apply nearly as well in North America as it seems at first glance.  I would guess that something like half of the readers of this wiki were alive at the time of notable abuses of the 'native americans' at the hands of (primarily) european descendants.  I include in this systemic violations, as well as specific instances.  And there are institutionalized problems that continue to this day.''
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CategoryHumanFactors