They have been having major wars since 1540 - 1924.
But just to name a few:
American Revolution (1775–1783)
Cherokee–American wars (1776–1794)
Northwest Indian War (1785–1795)
Nickajack Expedition (1794)
Sabine Expedition (1806)
War of 1812 (1811–1815) Tecumseh's War (1811–1813) ...
First Seminole War (1817–1818)
Winnebago War (1827)