I tend to lead towards the idea that one does not rely upon the other. While speech is being protected more and more, I do not believe that supporting (or protecting) free speech creates criminal behavior.

I like speamerfan's answer about the government not infringing on free speech and nothing is said about the individual. Nothing can stop me from disagreeing with something someone else says. This, though, is a far cry from bringing about criminal behavior.

Open and free speech does allow for irresponsible speech, however, the dangers of irresponsible and even evil speech can be diminished by the presence of a popular, critical voice.

When one message is publically aired and another is aired which reasonably interprets and comments upon the first, we won't have too many problems with the first message. The problems seem to arise when there is no second voice, no critical lens to parse out the rationality of the first message and either value or de-value the first message. 

While I agree that political correctness is rampant and quite odious, there seems to be some confusion about what the First Amendment protects.  The amendment guarantees that the government may not interfere with our speech, not that private individuals or entities may not do so.  If a person who is privately employed loses a job or a student is downgraded because of political views, those are decisions made by private actors, not by the government.  The First Amendment does not control those situations at all.  Additionally, there have always been limits to the First Amendment, for example, commercial speech being less protected than political speech, the government's right to sometimes control the time, place, and manner of speech, as in requiring permits for demonstrations and parades, and historically, no protection at all for obscenity, whatever that is. 

Some of the First Amendment rights were clearly eroded after 9/11 such as the government's right to investigate what is on computers at the public or school libraries. As an indication that there are things that are forbidden to say in the U.S., a few years ago Swiss tennis pro Martina Hingis complained that two American players who are sisters were given an inordinately high percentage of commercial endorsements and other pros made no commercials. Later, she was severely berated as making racist comments. So, she came on American TV and apologized, saying, "I am sorry; I am not from America; I did not know your laws." 

When there are "unwritten laws" that prohibit people from criticizing others without losing their jobs, positions, etc. then there no longer is freedom of speech.  After all, the very term "politically correct" points to the fact that people have lost certain freedoms.  Recently in the news, a football coach lost his job because he wrote a song that criticized negatively the president of the US. A few years ago, a prominent (and liberal) news magazine (Newsweek or Time) published an article a couple of years ago on how many Conservative Christian college students in various universities across the country who expressed their viewpoints in the classroom were graded poorly by their liberal professors.

With the erosion of First Amendment rights, there is, indeed, the possiblity of people's eventual arrests for saying or doing something that disagrees with those in power. Or, before this happens, we will have more of what already exists: the media destroys a person's good name with innuendoes, etc. After all, America has already had its Red Scare, has it not?

I am not clear on why there would be a relationship between free speech and violence, and I'm aware of no research that establishes such a connection.  Whether there is even a relationship between the exposure to violence in the media and violent behavior is uncertain.  But supposing for a moment that there is even a speculative connection, we must still balance the right to free speech against the possibility of violence.  What would we have to give up to avoid a potentially violent act?  This reminds me of The Giver, a novel that makes clear that protecting society against possible ills does not have a desirable outcome.  It also reminds me of the movie Minority Report, in which people are convicted for crimes they are thinking about.  Do we really want to live in a society in which we have repressed free speech because someone might commit violence?  Where would we draw the line?  Would this be up to the states or the federal  government to control?  Once you allow a government to control speech for any reason, it's a slippery slope to the government repressing speech that criticizes it.  There are countries in which this is the case, and I haven't noticed that they have less crime than we do.  

I believe we have gone too far with progressivism and permissiveness. I believe that the unrestraint prevalent in America creates an environment to "criminalistic behavior." Our educational systems are part of the problem, but the news media, with the thirst for sensationalism and the "personal story behind the story," and the entertainment media are guilty participants in the new environment. To prove the point, a film that sports a vocabulary of one f-word and is drenched in cold-hearted violence must be judged under a very perverted definition of "good" to have won Academy Awards. Actors are correct when some say they will not take any roles that included the portrayal of violence because those actions would be imitated across the country by young and/or unthinking people.

Are you talking about some particular aspect of society, or are you asking this in general?

It is hard to argue, for the most part, that free speech makes for "criminalistic" behavior.  You might say that free speech (like that of the Westboro church) makes for a less harmonious and cohesive society.  Or you might say that free speech (the right to have actors say fairly "dirty" things on TV) reduces the level of morality in our society.  But it is hard to say that free speech leads to criminality.