An earthquake is a very deadly disaster. In some games, earthquakes damage the entire city and anything underground.
In SimCity 4, it only affects a long horizontal area but is much more destructive. Instead of the AI picking random buildings to destroy, all buildings along the damage line are destroyed, regardless of how damaged they are. Depending on the player, most earthquakes only travel a few blocks, but if the player holds the earthquake option they can increase the damage by climbing up the Richter Scale. But if the player holds it too long it may result having the quake be a normal moderate damaging quake, (possibly a bug), but in most cases it will turn out to be a very big and disastrous quake.
Earthquakes may create aftershocks in SimCity Societies, and will target random buildings to collapse.
SimCity Creator DS
In SimCity Creator DS, earthquakes can happen very rarely in Open Asia Age, and frequently in the Global Warming Age. The earthquakes strike everywhere in the town and destroy random buildings.
In SC'13, simply click in the area you want the earthquake to happen. The ground will first shake, with people screaming and glass breaking. Soon after that, an aftershock may or may not occur which will target random buildings around the area and completely obliterate them, causing the deaths of sims. They are lost, but not forgotten.