I know you probably didn't mean it, but the only South American civ we got is the Inca.
Nevertheless, it's hard to give the North American Indians you mentioned the same weight the Inca, Mayans and Aztecs had in history; they may be great in Western Genre and USA national history, but I must say the Iroquois is just enough.
Yep of the
overall greatest of Native American Civs (not looking at regional greantess) I say some of the most important have already been included.
A few select more I consider as the most important:
1. Chachapoya important power that brokered trade and power between Andes and Amazon. Built large cities engaged in warfare against the major powers for centuries (Inca, Huari, Spanish, etc.)
2. Toltec have been mentioned as well. They will never get in and I have never mentioned them but they are an interesting and important civ too. Tulum and their civilization shaped Mesoamerica greatly introducing the main forms of Human Sacrifice we know today of the region, the Great Prophet/Military leader Topiltzin Quetzalcoatl shaped Mesoamerican religion and power as we knew it last. City style great changed due to the Toltecs, etc. Very influential but area is overlapped and will never be included
3. The Pueblo/Anasazi. Built a complex agricultural system, interesting architecture, and dominant in influence in their region. Not as important as the first two mentioned but still very important due to trade and interaction.
Those 3 are my top important ones still not included (doesn't mean they will).
There are others that are also interesting possibilites:
Comanche, Illinois,
Sioux, Carib/Taino/Arawak,
Mississippians,
Zapotec, Cherokee, Apache, Navajo, Tupi, Tuscarora, Seminole, etc. that would all be interesting on their own rights but that I don't think of as important influence wise. The most important of these lesser ones are bolded. Older civs like the Huari, Teotihuacan, Nazca, etc. I didn't list even though they were extremely important because their date is too old to ever truly be considered appropriately for a civ (language problems exist, city list, direct knowledge of some aspects, etc. But although if the Huns got in I guess I shouldn't ignore them)