Generally, protests are carried out against immoral and unjust actions. If protests are violent, they could be immoral themselves or a source of injustice. Therefore, they will not be effective because they are like the very thing that they are protesting against. Due to this, non-violent protests are more effective than violent protests.
The first historical example which comes to mind is the British colonialism of the United States. The Americans could not peacefully protest against this because the British had an army behind them and violently opposed any protests to their presence in the United States. Therefore, the only form of protest which could achieve the removal of the British from America was violence.
The second historical example which comes to mind is the secession of the Confederate States. The North and all Americans who opposed the division of their country into two could not protest against this in a non-violent way. The confederate states had gathered their armies and had declared their secession from the United States of America. The only way that this development could be reversed was through violence, which means that protest had to take the form of military confrontation.
The type of direct action which martin Luther King called for was peaceful protest in the form of sit-ins and marches.