Electric stoves do not use natural gas, only electricity. When you accidentally leave your gas stove or oven on, you can smell the gas, which alerts you to turn it off. This is not the case with electric stoves; they are silent and odorless, thus easier to leave on inadvertently, creating a fire hazard.
Some electric ovens have been recalled because they turn on spontaneously. This presents another fire hazard. The heat can catch anything on fire that is flammable in the oven or possibly even near it. To avoid this hazard, keep your stove and surrounding areas clean and free of clutter. If you have received a recall notice, do not ignore it.
With gas stoves you can see how much heat an item is receiving by the size of the flame. With electric stoves, all you see are bright coils, which doesn't necessarily indicate how much heat is being delivered. This means that something you intended to cook lightly can catch fire if the heat is turned up too high. For example, if you leave something to simmer and walk out of the room, it can boil over if the burner is set too high.
The heat on the surface of an electric stove is another danger. Especially with the flat-top stoves, you can burn yourself if you are not aware that the stove had just been on. This is particularly important to note if you have small children, because they will just see the surface as it typically looks, even though it may actually be very hot. When the flame on a gas stove is turned off, the surface cools down much more quickly.