Boudin was a prominent civil liberties lawyer whose clients included Paul Robeson, Benjamin Spock, and Pentagon Papers whistleblower Daniel Ellsberg.

He argued and won several landmark U.S. Supreme Court cases, including: Kent v. Dulles (1958), which protected Americans' right to travel abroad • Aptheker v. Secretary of State (1964), which struck down a law provision barring Communist Party members from getting passports • Lamont v. Postmaster General (1965), which ruled unconstitutional a statute requiring the post office to detain "communist political propaganda" unless the recipient requested it