My reaction to the word Indian would be pretty similar to the other North Americans who responded, in particular Bean. I was surprised to note that someone mentioned the word autochtone as a description of indiginous persons; I am familiar with that being used in French but never in English.
I will admit to some difficulty with the term native, as I am a native Canadian albeit a caucasian one. I was born here in this country, therefore I am a native of Canada. How many generations back must your family trace its roots before its progeny can be called native? Are the descendants of William the Conquerer living in England today to be considered immigrants? Not an easy question, but one that bears some thought.
Finally, an example of how our sensibilities have changed can be seen in the changing titles of Agatha Christie's "And Then There Were None." It started out as "Ten Little N*****s" and then became "Ten Little Indians" before changing to its current form.
