By Native Americans, do you strictly mean North American natives or would you also include Mesoamericans or South Americans? Mesoamericans invented maize and Andeans invented the potato. Those are fundamentals of modern agriculture.

hi! a similar question came up recently; check it out!

• Were there any inventions or tools Europeans have adopted from Native Americans? - a good starting point is this response by /u/Reedstilt

The idea of a confederacy of states. Benjamin Franklin took this idea from the Iroquois Confederacy of what is now upstate New York (approximately) and presented it to the states as a way to have both independent existence as states and as part of a larger group -- the United States of America organized first under the Articles of Confederation. The national government turned out to be not strong enough and so the Articles of Confederation were replaced by the United States Constitution a decade later. For more, much more, read the book Indian Givers: How Native Americans Transformed the World. http://www.amazon.com/Indian-Givers-Native-Americans-Transformed/dp/0307717151

Not quite the answer you are looking for, but Native Americans provided encryption during WWII. As it turns out, no one in the Axis nations had studied Native American languages, so all they had to do to encrypt a message was to speak it in whatever language that tribe spoke. They also encrypted messages by using a taking the first letter of a English word, and saying it in their native language, (the letter A could be the native word for apple, amber, axe, etc.)

This encryption method was never broken in WWII.

Please read Jack Weatherford's Indian Givers: How the Indians of the Americas Transformed the World. Besides a large portion of the world's food crops that enabled the world population to dramatically increase after the Columbian exchange, Native Americans also provided a large number of the world's plant-based pharmaceuticals, commonly known examples being quinine and slippery elm.

The League of Iroquois contributed one of the longest continuing democratic governments in the world (along with Iceland).

Many words in American English are on Native origin (woodchuck, squash, chickadee, barbecue, hurricane, tomato, peyote, coyote, hammocks, atlatl, etc. etc.) The state language of Paraguay is Guaraní and the state language of Greenland is Kalaallisut—both Indigenous languages.

Kayaks are an Indigenous invention (obviously the materials have changed over time). We created some of the world's largest ancient cities, such as Tenochtitlan and Chan Chan. The Andes represents one of the longest continuing textile traditions in the world with some of the most sophisticated weaving techniques.

Native Americans independently invented government, cities, agriculture (in at least three different locations), and writing. Poetry, dance, visual arts, diplomatics.

My grandfather helped design the navigational system for the B-52 bomber and invented a fuel-injection system, so there's that.