This is a new standard for household wiring. It called Non-metalic or NM cable. The newest of such a kind of wiring is NM-B and when you have new wiring installed this is what you would get.
Important for your wallet is that when this wiring is installed properly it should last for decades because it is really reliable.
Romex always has a ground wire, what makes it safer in two important ways:
Outer jacket of this type of wiring is slippery and this makes installation easier, but the cable seems to be soft and can be easily damaged. The cable should be run through the very center of the studs.
It requires to be 1 1⁄4 inches from the face of the stud on both sides. When it is not possible there should be a steel plate (nail guard) put over wire to prevent from using a nail or screw there.
If you see that your service panel is full of romex wires you can be sure that the wiring is not old and is not rotting.
However if something seems wrong you should call specialists to check the problem – electricity is deadly when in not in professional hands.