In fact, a single dose of paracetamol (known as acetaminophen or Tylenol in the US) can kill a cat. Other human pain medications, such as ibuprofen and naproxen, also are not safe and should never be administered to cats.
As any cat lover can attest, cats are very unique creatures. This applies to their metabolism and physiology, as well as their more visible traits. Because of this, I recommend against giving any sort of medication to your cat without consulting a veterinarian first.
Although dogs are less sensitive than cats, most human painkillers and other medications should not be given to them, either.
A wide variety of painkillers is available through veterinarians for use in dogs. Unfortunately, the options for cats are much more limited. A great deal of effort is being put into developing pain management solutions for cats, and in my opinion success cannot come soon enough.