I find that it's always interesting to THEN consider, okay -- while there's no centralized board or anything -- what does e.g. American censorship go after?
The American way is voluntary self-censorship for commercial purposes. This makes it much harder to say what exactly is allowed and not, because it is easy to see what scenes have been cut from a show but it is impossible to say what scenes was never written or produced. Even blatant censorship like the Hayes Code or the Comics Code was never enforced by the government and therefore never in conflict with the 5th ame…
The US government hasn't been able to resist censorship entirely. Comedians have been arrested for "obscenity". The FCC will happily go after certain violations in TV and radio. The US government has also censored news broadcasts and journalists.
Bush in particular was very aggressive in censoring the news coverage of his war. Most notably, the flag-draped coffins of dead American soldiers were banned from TV news. During the Regan administration the Justice Department also briefly banned the Canadian film "If You Love This Planet" for being "foreign political propaganda".