Hays took part in numerous notable cases, including the Sweet segregation case in Detroit as well as the Scopes trial (often called the "monkey trial") in 1925, in which a school teacher in Tennessee was tried for teaching evolution; the "American Mercury" censorship case (1926); the Sacco and Vanzetti case, in which two Italian anarchists in Boston were convicted and executed in 1927 for a murder they denied committing; and the Scottsboro case, in which eight black men from Alabama were convicted and sentenced to death in 1931 for allegedly attacking two white women. Hays attended the Reichstag trial in Berlin on behalf of Georgi Dimitrov, a Bulgarian Communist accused by the Nazis in 1933 of burning the Reichstag.