A riot happens if a city's population becomes very unhappy with the mayor's choices, or if they are being deprived of essential services, such as a prolonged blackout, and although uncommon, lack of sanitation services. Riots can be subdued very quickly if police response is immediate, however, they will cause massive amounts of damage to buildings and infrastructure if left alone.

During the rioting, Sims will wander around the town/city's streets, looting from stores, throwing rubbish around, and in later stages, jumping on and turning over cars, as well as occasionally throwing objects that look and behave like Molotov cocktails, which (without proper fire coverage) may ignite surrounding buildings, causing destructive fires, if left unattended. 

If the riot is not subdued quickly, the size of the riot may increase, sometimes up to almost 20 tiles away (about 3 to 4 city blocks) from the original starting point. Sims will sometimes leave the roads and riot on private property, although this may simply be an error when they initially spawned.

In SimCity 2000, A variation exists called "Mass Riots", which is accessible from the Debug menu. This is essentially the same as the normal "Riot" disaster, but even more groups of rioters will initially spawn, making it harder to subdue their city-wide rampage.

Tips

• Riots are very rare; with even a poorly governed city, it is highly unlikely that the player will ever experience a riot without the help of external modifications. 
• Preferably don't try to drive a firetruck to extinguish fires yourself; aside from the fact that it's not practical, there is a glitch where sometimes you will have some difficulty deploying firemen around large groups of rioters.
• Riots will not occur within the radius of a police station, and any new station will automatically disperse existing riots.
• Rioters can cross bridges, so it's recommended that the player demolishes them when a riot breaks out to prevent them from spreading to other sections of the city, and then rebuild them once the rioters are dealt with. Other desirable options are to demolish any nearby buildings you can afford to rebuild later so that they can't be burned down, and/or place Water on blank tiles to isolate rioters and stop them from moving around before dispatching Police/Military to apprehend them.
• If rioters have already burned/overrun a significant portion of a city and their groups have multiplied to the point where they are swarming over an entire area, it is recommended not to dispatch Police/Miltary (since the rioting groups will multiply too quickly to catch them all) and instead utilize the Bulldozer tool to lower the terrain on top of the rioters until water replaces the ground, effectively "drowning" them.