Both dogs and cats need identification. Even if your cat is a 100% indoor cat, she still needs ID - scared or excited pets can slip out the door before you can stop them.
Check with your city for any licensing or identification requirements for your pet. Here are three choices. A combination of them is best just in case one form of ID fails.
License tag. Usually purchased from the city, your pet is assigned a number which is tracked in a computer database. Tags are attached to your pet's collar. If your pet is found, the animal control officer can check the tag number, pull up your address, and call you to let you know they have your pet.
The disadvantages to using a tag are: the tag can fall off and get lost; it might not be readable; your pet may not always be wearing its collar; your pet may slip out of or lose its collar.
Tattoo. Tattoos are commonly etched into one of your pet's ears during spay/neuter surgery (pets must be under anesthetic for this procedure). Tattoos are a visible and somewhat permanent method of identification.
Unlike tags, tattoos are not reliant on your pet wearing its collar. However tattoos usually fade over time, making them illegible. They can be retraced ... but since pets must be under anesthetic and there is always a risk with anesthetic, retracing a tattoo should be done at the same time your pet is undergoing another procedure anyways.
Microchip. A microchip is a small, electronic chip (approximately the size of a grain of rice) that is implanted just under your pet's skin. It is administered quickly and painlessly by a simple injection.
Microchips each have an identification number associated with them. Along with this ID number, your name, address, and phone number are entered into a computer database. If your pet gets lost, animal shelters or city pounds equipped with scanners will be able to scan your pet's body to quickly locate the ID number of the microchip along with the corresponding owner information. Many shelters and pounds these days are equipped to handle microchips.