My maternal grandmother was half Native American - some tribe from upstate New York as I recall. I've never had the inclination to research or document it, though.
Funny, I am in the exact same position. My maternal grandmother was half Cree. Just found out about that recently.
Many Americans may have some Native American blood. My paternal Grandfather hailed from Virginia and had family in Oklahoma, there is a picture of my father's Great-Grandmother who was pure Cherokee (yes Cherokee for those of you who don't believe that Cherokees intermarried with the white devil) and tales are told about her mean-streak. None of the kids in the family liked to get too close, they might get a knock up the side of the head just for looking cross-eyed at her. On my Mother's side of the family we have her Grandmother who was from Quebec and was French-Indian ancestry. I have a photo of her Great Grandmother who was Indian, married name: Ludivine Barbeau. Not sure of her tribe, but she did exist.
Some of my siblings, myself, my nieces, nephews etc... have some Native American physical features, including some who have the skin coloring. I have never been interested in joining a tribe, but I'm not about to deny my ancestry. I did attend a pow-wow once while visiting friends in New Mexico, but only as a tourist.