The "dropping a plugged-in appliance in a bathtub" myth is a classic, but the science behind it is a lot more complicated than what you see in the movies.
The danger is absolutely real, but modern safety features like ground fault circuit interrupters are designed to prevent it. If it detects even a tiny difference, meaning some current is going somewhere it shouldn't, it shuts off the power instantly. So, if an appliance were to fall in the water, the GFCI would trip before any serious harm could be done.