Congress imposed our current income tax structure through the 16th Amendment to the U.S. Constitution. The dispute by many today is over whether or not the necessary 3/4 of the states ratified this Amendment in 1913.
The short answer is, yes, individuals and businesses must file federal income tax returns. Citizens who work outside the U.S. must also file federal income tax returns.
From the Internal Revenue Service (IRS) Bulletin: "The function of the Internal Revenue Service is to administer the Internal Revenue Code. Tax policy for raising revenue is determined by Congress."(2nd link below)
Each state has its own laws and many also impose an income tax requirement on its residents. See the 3rd link below for a breakdown of state income tax requirements.