Because rioting is a criminal offence in most jurisdictions, the conduct must be defined and there are therefore, as many definitions as there are jurisdictions.
Historically, at common law, riot had but one definition and most criminal statutes derive their particular definitions from it.
This common law definition was aptly summarized in the English decision Field v Receiver of Metropolitan Police,  2 KB 859 as follows:
“There are five necessary elements of a riot (i) number of persons, three at least; (ii) common purpose; (iii) execution or inception of the common purpose; (iv) an intent to help one another by force if necessary against any person who may oppose them in the execution of their common purpose; (v) force or violence not merely used in demolishing, but displayed in such a manner as to alarm at least one person of reasonable firmness and courage.”
In Dictionary of English Law (London: Sweet and Maxwell, 1923) author W. J. Byrne defines riot as:
“A riot is an unlawful assembly which has actually begun to execute the purpose for which it assembled by a breach of the peace and to the terror of the public.
"A lawful assembly may become a riot if the persons assembled form, and proceed to execute, an unlawful purpose, to the terror of the people, although they had not that purpose when they assembled.”
John Bouvier’s 1856 (American) Law Dictionary adds:
“If a number of persons lawfully met together, as, for example, at a fire, or in a theater or a church, should suddenly quarrel and fight, the offense is an affray, and not a riot, because there was no unlawful assembly.
"But if three or more being so assembled, on a dispute occurring, form into parties with promises of mutual assistance, which promises may be expressed or implied from the circumstances, then the offense will no longer be an affray but a riot... in this manner any lawful assembly may be converted into a riot.”
One can see vestiges of the common law definition in the United States Code, Title 18, Part 1, Chapter 102, §2102, which defines a riot as:
“...a public disturbance involving (1) an act or acts of violence by one or more persons part of an assemblage of three or more persons, which act or acts shall constitute a clear and present danger of, or shall result in, damage or injury to the property of any other person or to the person of any other individual, or (2) a threat or threats of the commission of an act or acts of violence by one or more persons part of an assemblage of three or more persons having, individually or collectively, the ability of immediate execution of such threat or threats, where the performance of the threatened act or acts of violence would constitute a clear and present danger of, or would result in, damage or injury to the property of any other person or to the person of any other individual.
“’to incite a riot’, or ‘to organize, promote, encourage, participate in, or carry on a riot’, includes, but is not limited to, urging or instigating other persons to riot, but shall not be deemed to mean the mere oral or written advocacy of ideas or expression of belief, not involving advocacy of any act or acts of violence or assertion of the rightness of, or the right to commit, any such act or acts.”
At common law, there was even an intermediary offence between an unlawful assembly and a riot: a rout, or an unlawful assembly which has taken some initiative towards the execution of the common purpose.
Canada's Criminal Code defines and prohibits both unlawful assemblies and riots but defines the latter in relation to the former, as follows:
“A riot is an unlawful assembly that has begun to disturb the peace tumultuously.”