Scarface
Not to be confused with Al Pacino's Scarface, although it's based on the same dude. This Scarface came out in 1932, and it genuinely rivals the violent nature of the newer one. For that reason, this movie got banned in five states and five cities.
The Exorcist
This movie was banned in the United Kingdom before it even got released. Audience members (remember, this is 1973) were reported leaving the movie theater in hysterics, vomiting, and uncontrollably shaking. This movie was even banned in places in the US for a long time. Nowadays, The Exorcist is considered a horror essential.