Libel and defamation are the main exceptions to First Amendment protections. For instance, if someone was spreading lies about another person that damaged the victim's reputation, the victim could sue and the court would support them. There have also been exceptions made for speech that incites violence, as well as the proverbial "yelling 'fire' in a crowded theater." Death threats, then, are usually taken seriously by law enforcement as statements of intent, and people who call in false bomb threats are invariably arrested. As you can see, a common theme here is lies—the Founding Fathers wanted to ensure that free speech didn't mean that there was no check on misinformation.