In particular I'm curious about North American tribes.
In the old world the spear generally played a pretty centric role in warfare. In China and Japan tactics often included large components of spearmen supported by archers. In Europe, even before the era of pike and shot, bows generally played only supporting role while most of the mixed infantry were armed with polearms.
Was early America the same, or would warfare have looked more like it does in a wild west shootout but with bows instead of guns?
This is a tepoztopilli, or at least an engraving of one that was previously kept in the Royal Armory of Madrid (it was destroyed in a fire along with a matching macuahuitl). This is represents a finely crafted example, which was may have been made specifically for show. The general layout is consistent with examples seen in art work of the time, though the shaft is particularly truncated.
A more typical tepoztopilli would be about 5-7 feet long, with about of foot of that being a cutting surface of inset obsidian blades. Like the macuahuitl, this was a slashing weapon, though obviously one that has gotten considerably less attention than that prestige weapon.
As for the exact deployment of the spears on the battlefield, we are somewhat stymied by the fact that first hand accounts by the Spanish tend to be not detailed in the way we want them to be, and later Nahuatl sources are similarly focused on more important things than detailed descriptions of the order and disposition of military forces. Ross Hassig, who literally wrote the book on Aztec warfare, has done the heavy lifting of gleaning materials from pictorial and literary depictions and sussing out how they might work in more practical terms.
Per Hassig, while the elite upper crust of soldiers would be wielding macuahuitls, they would be flanked by more novice soldiers with tepoztopillis. After an initial barrage of sling stones and arrows, these melee troops would close the distance, with the macuahuitl troops hurling atl-atl darts (which I am assuming you would want to discount from the "melee spear" category) as they advanced. The line of battle would then consist of a backbone of tepoztopilli studded with macuahuitl trying to break that line.
I wrote about this and more logistical aspects of Aztec warfare in this ancient comment, if you'd like some more reading material.
The North American tribes (north of Mexico that is) did not, to my knowledge, fight in formations with shields and spears (like the classical phalanx formations). They did utilize spears, but also bows, hatchets, and knives. Much of their tactics depended upon surprise rather than fixed battle formations. Most of the eastern continent at that time was heavily wooded, with not a lot of open clearings, so the fighting was guerrilla style.
The advent of horses in the western plains changed warfare dramatically for tribes such as the Comanche, Apache, and Sioux. The style of fighting from horseback with a bow and arrow was practically unbeatable. This style had similarities to the Eastern European/Western Asian Steppe fighters who were so devastating against the Chinese and Russians during the middle ages. Before the 1860's the standard rifle could only fire one shot. A man with a rifle was no match for a group of Indians on horseback shooting arrows.
With the advent of the repeating rifle, combined with horseback riding, tribes like the Apache and Sioux were able to hold off the US military for a short while. However, the repeating rifles could be used effectively from the ground, behind protective cover, to shoot riders off of horseback.
