Let's dig into the "Bill of Rights", starting with the 1st Amendment

When our Founding Fathers were replacing the Articles of Confederation and Perpetual Union (aka the Articles of Confederation) with the new Constitution of the United States, there were some major issues revolving around the guaranteeing of individual rights as well as the constraining of the power of the federal government.  In order to get the basic Constitution adopted, the various states' representative had to hash out a guarantee that, immediately upon the adoption of the Constitution in 1789, there would be a set of amendments that would guarantee those individual rights.  This led to the first 10 Amendments which were authored between 1789 and 1791, when they were adopted.

The First Amendment states that "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."  This is the Amendment that is used by many to protect their right to protest (no matter how profanely), harangue crowds, write articles (in newspapers, magazines, or even blogs), and otherwise "make their voices heard".  It has also been used as the basis for removing any references to God or the Ten Commandments from public facilities and even to ban the Pledge of Allegiance in schools ... which sort of makes an interesting comment about the phrase "free exercise thereof". ;-) 

Of course, there are some constraints that have been allowed on this right.  For instance, courts have ruled that one can't shout "Fire!" in a crowded theater unless, of course, there is actually a fire.  In other words, the government has the right to constrain the rights guaranteed by the Bill of Rights where it is "reasonable" to do so to prevent the rights of an individual from causing problems with the overall community's safety.  The government's ability to constrain, though, are extremely limited because the government has the burden of proving the reasonableness and necessity of those constraints (e.g., in the case of yell "Fire!" in a crowded theater when there is no fire, the necessity is based upon the panic and subsequent dangers to innocent attendees who might get injured in the subsequent flight from the theater).

Another aspect to consider is the phrase the right of the people peaceably to assemble.  This portion of the First Amendment has recently been used to excuse/justify the various protest marches around this nation.  Cities around the nation have enacted ordinances that require those who would hold rallies and, especially, marches to submit requests for permits to do so, not because the protesters don't have the right to do so but, rather, because there is a need to provide for the safety of both the protesters and other citizens during the protest.  When marches occupy city streets, those streets have to be blocked off in order to prevent drivers from accidentally driving into (or over) the crowds that are marching.  Also, there is a need to contain the protest march so that it doesn't interfere with the functioning of society.  This has, at least traditionally, been considered to be a "reasonable and prudent" constraint upon the rights of those who would gather to protest.

However, of late, there appears to be an assumption by those who would gather/assemble and march in protest that their right to protest supersedes the rights of everyone else to conduct the business of society and that any constraints on that right to march in protest is unreasonable.  As a result, whether or not the marchers choose to submit requests for permits to march, these protesters consider it unreasonable to require them to limit their activity to certain streets, much less to not shut down highways, airports, or business activities.  This is to say nothing of the peaceful constraint contained within the First Amendment.  In general, many have extended their "personal rights" to not only supersede the rights of others but to also include the destruction or appropriation of the property of others as a form of "protest".

Traditionally, when a large group of individuals engages in unconstrained, especially unconstrained and violent, gathering and obstruction of the functioning of society, they have been termed a mob and when they have engaged in the destruction or "appropriation" (aka stealing and looting) of other peoples' property, the term "rioting" has been employed to describe their activities.