Do you know what a ground cable is for? The main purpose of it is to protect you from electrocution. When there is a malfunction in an electrical appliance, the current could travel through you and cause serious damage, even death. The ground cable provides an alternate route for the current to reach the ground, thus saving your life.
In some older homes, you will still find wall receptacles that are ungrounded, and this could cause a problem. Even worse, some homeowners have taken grounded receptacles and installed them even though there is no proper ground there. This could prove to be very dangerous.
Another side effect of a missing ground is that some appliances won’t work properly. Even a surge protector will not properly protect your appliances when plugged into an ungrounded receptacle.
You could install a GFCI receptacle to get the protection against electrocution when your receptacles don’t have the proper wiring.