Residential electric stoves are designed to be used in homes and are generally considered safe. Since electric stoves don't have an open flame, they're also considered safer than gas stoves.
Electric stoves typically have a number of fuses to prevent electrical problems. Many also have thermal fuses that shut heating elements off if they overheat. Newer safety features help mitigate some of the risks of using electric stoves. Automatic shutoff capabilities, for example, turn cooktops off if they are not in use for an extended period of time. Control locks prevent the stove from being turned on until it's unlocked. Some stoves even have motion detectors that turn the system off if nobody is in the kitchen.