Terminology
Historians often comment on mob rule as a factor in the rise of Rome and its maintenance, as the city of Rome itself was large − between 100,000 and 250,000 citizens − while the aristocracy and even military was very small by comparison to the citizenry. With weapons also being crude, the military force did not exist that could have dealt with a revolt from the larger populace. There was a constant need to keep people fed, distracted, and in awe of the power of the state. Those who could do this, ruled not only Rome, but the whole of the Roman Empire.
Lapses in this control often led to loss of power, or even the loss of heads, of officials − most notably in the reign of Commodus when Cleander unwisely used the Praetorian Guard against a mob which had come to call for his head. As Edward Gibbon relates it,
The people... demanded with angry clamors the head of the public enemy. Cleander, who commanded the Praetorian Guards, ordered a body of cavalry to sally forth and disperse the seditious multitude. The multitude fled with precipitation towards the city; several were slain, and many more were trampled to death; but when the cavalry entered the streets their pursuit was checked by a shower of stones and darts from the roofs and windows of the houses. The foot guards, who had long been jealous of the prerogatives and insolence of the Praetorian cavalry, embraced the party of the people. The tumult became a regular engagement and threatened a general massacre. The Praetorians at length gave way, oppressed with numbers; and the tide of popular fury returned with redoubled violence against the gates of the palace, where Commodus lay dissolved in luxury and alone unconscious of the civil war... Commodus started from his dream of pleasure and commanded that the head of Cleander should be thrown out to the people. The desired spectacle instantly appeased the tumult...
This followed a previous incident in which the legions of Britain had demanded and received the death of Perennis, the prior administrator. The mob thus realized that it had every chance of success.

Mobs in history
During the French Revolution, the mobs in Paris played a similar function, but were more carefully manipulated by political leaders who sensed that they had the power to dispose of monarchy entirely, as they did, eventually setting up a representative democracy (which in turn fell to Napoleon's model of semi-constitutional monarchy).
The modern theories of civil disobedience and satyagraha bear some resemblance to mob rule and its mechanics. Certainly it is quite frightening for large numbers of people, even peaceful ones, to be marching and shouting common demands, if one is charged with the uncomfortable task of refusing them. If Roman guards, facing crucifixion for disobedience, could be swayed by mobs, it is obviously possible also to sway modern police even in a police state. The 1986 EDSA Revolution in the Philippines, the Velvet Revolution in former Czechoslovakia, and the resistance to the military coup in the Soviet Union in 1991 that led to the collapse of that state, are situations where it is possible that it was the "mob" which won the day due to defections by authority.
Whether by intent or by circumstance, non-violent well-organized assemblies often degrade into unruly mobs. Provocation from within (such as an agent provocateur) and from external forces is often a factor, but crowd dynamics often spontaneously emerge to confront the peaceful intentions of those who rallied a crowd. Published treatises on civil disobedience theory almost always encourage practitioners to establish order within their ranks, but civil disobedience groups often face difficulty in controlling those they recruit. Dr. Martin Luther King, a renowned advocate of orderly demonstrations of group power, died after he returned to Memphis to restore order to demonstrations he had inspired but which had turned violent on his previous visit.

Mobs used to affect policy
A scenario where mob pressure did not win can be seen in the incidents of the Tiananmen Square protests of 1989. While Beijing-based units of the People's Liberation Army initially refused to charge on the students occupying the square, new units from the countryside were brought in, who tended to perceive the students not as citizens like themselves, but as people deluded by a privileged position in Chinese society. As soldiers fought their way through barricades and through a downtown area occupied by a now-leaderless throng, combat injuries and injuries from indirect gunfire in an urban setting resulted in deaths. The dead and injured included Beijing residents, PLA soldiers and students who had left the square to enforce barricades around the city.
As this example shows, relying on sheer mob strength and disruption is chancy in any political movement, and may not to be relied upon for any extended period. Encounters with mob rule usually hinge on threats of bodily harm - do what the mob wants, and you won't get hurt; resist, and you almost certainly will - the sheer size and psychological makeup of the mob makes it difficult or impossible to assign blame to any one person. The morality of the mob and its actions can be said to depend on what its demands are, what it's being influenced by, and what it's fighting against. While most people would find it objectionable for a mob to cause harm to ordinary citizens, the same cannot be said about a mob rising up to depose a tyrant; unfortunately these distinctions can be lost in the passions of the throng.

Other mobs

Bandwagon effect
Collective consciousness
Collective effervescence
Collective hysteria
Collective intelligence
Crowd
Crowd psychology
Flash mob
Group (sociology)
Group behaviour
Herd behaviour
Herd instinct
Herd morality (Friedrich Nietzsche)
Keeping up with the Joneses
Lynching
Peer pressure
Sheeple
Smart mob
Social comparison theory
Spiral of silence
Tribalism