Step 1: Compare candidate rivers.
The Missouri River and the Mississippi River are the two rivers usually compared for this title; measured on its own from source to mouth, the Missouri is the longer of the two individual rivers in the United States.
Step 2: State the answer, with the common alternative noted.
The Missouri River, at about 3,767 kilometres, is the longest individual river in the USA; the combined Mississippi-Missouri river system (about 3,766 km after their confluence) is also frequently cited in this context.
Final Answer:
The Missouri River is the longest river of the United States of America.\[ \boxed{\text{Missouri River}} \]