Don't risk losing your feline friend forever. Please put a collar on your cat and an identification tag with your name, address and phone number. Be sure to keep the information current. You'll want to tag your cat even if you never let it go outside because there is always the chance that it could slip through an open door or window and become lost.
There are collars made especially for cats with a short piece of elastic sewn in. These "break-away" collars can be buckled snugly around the cat's neck, but will stretch and let the cat escape if it should get hung up on a tree limb or fence. It's important to remember that many more cats have died because they were lost and their owners couldn't find them, than have ever been injured from wearing a collar.
The first time you put a collar on your cat, give it a catnip-filled toy. The toy will distract the cat's attention from the odd feeling of wearing a collar and by the time it finishes shredding the toy, it may have forgotten the collar entirely.