I'm no Constitutional lawyer, but from what I remember, there are quite a few exceptions to free speech. The most important point to keep in mind is in the text of the First Amendment itself. The First Amendment only applies to State Action, i.e. the State (Feds through the First amendment, States through the 14th). So the state can't pass laws that infringe on free speech. However, they can pass laws restricting free speech where, (1) the law is content neutral, (2) the motivation for the law is unrelated to the "suppression of free expression", and (3) the suppression of free expression is an incidental side effect of the law. For instance, most cities have laws prohibiting loud noises after a certain time at night. This certainly infringes on free expression, but the law is content neutral (i.e. doesn't prohibit certain viewpoints, only any loud noises), the motivation is to keep things quiet so people can get their sleep and the suppression is incidental.

Other exceptions include: defamation (slander and libel), hate speech (e.g. burning crosses in people's yards), causing panic (e.g. yelling fire in a crowded theater), fighting words (words whose very utterance cause harm, e.g. racial slurs said right to someone's face), obsenity, incitement (e.g. soliciting a person to commit a crime).
In this case, the family of the soldier sued under several tort theories (intentional infliction of emotion distress, intrusion upon seclusion among others). The Defendant's defended by arguing that their speech was protected (so, they argue the state action here was the Court by deciding against them). In such a situation the Court has to look at the nature of the two side's interests (i.e. weigh the nature of the speech against the privacy interests of the family).

When engaging in this kind of weighing, the Courts look at the nature, place and manner of the speech. where the speech concerns a public interest and is in a traditional public forum, the Court will give such speech the greatest protection it can. As Justice Roberts said, "Westboro addressed matters of public import on public property, in a peaceful manner, in full compliance with the guidance of local officials." When the speech is on a public matter, in a public place and abides by other local laws which incidentally govern speech, and said speech does not fall in one of the traditional exceptions, it is almost impossible to hold that said speech can give rise to civil liability.

A good analogy would be the right that KKK members have to publicly assemble and disseminate their "literature". I think most people find their ideas repugnant, but that is all part and parcel of free society and free speech.

A completely agree with the decision, but I also see Justice Alito's point in dissent.

"This Court has recognized that words may by their very utterance inflict injury and that the First Amendment does not shield utterances that form“no essential part of any exposition of ideas, and are of such slight social value as a step to truth that any benefit that may be derived from them is clearly outweighed by the social interest in order and morality. . . . When grave injury is intentionally inflicted by means of an attack like the one at issue here, the First Amendment should not interfere with recovery. (internal citations omitted). . . . In light of this evidence, it is abundantly clear that respondents, going far beyond commentary on matters of public concern, specifically attacked Matthew Snyder because (1) he was a Catholic and (2) he was a member of the United States military. Both Matthew and petitioner were private figures, and this attack was not speech on a matter of public concern."

Why not fit this conduct into the exception for fighting words? Intentional infliction of emotional distress itself is usually done through words. The difference, in my opinion, is the nature of the speech (on a public matter) and the location of the speech (traditional public forum).

It's not that free speech is restricted to matters of public concern. The point is the level of scrutiny the Court gives to State action restricting the speech. It's a weighing of the interests issue. Where the speech concerns a public interest the Courts will apply "strict scrutiny" to the State action. Basically the Court has decided that speech that is of public concern should be given greater protection than other speech. As an example, calling a person a fascist, to his face, is fighting words (that was the fact scenario in Chaplinsky v. New Hampshire the case defining fighting words). Those words' sole point is to provoke and insult that person. That is very different than staging a public protest over a public matter.

Unfortunately, you don't have the right to call a person a fucking dumbass if, in doing so, your words are likely to provoke an immediate and publicly disruptive response. doing so can subject you to state criminal laws (see local criminal mischief statutes).

See this link (the first gray shaded block) for a good synopsis of fighting words and freedom of speech. http://www.lawsonry.com/2011/01/was-jared-lee-loughner-a-right-wing-extremist/