The most recent survey of American pet owners established that 85.8 million cats are owned in the United States, and that 42.9 million households in the United States have a cat. (American Pet Products Association, 2015-2016 APPA National Pet Owners Survey Statistics: Pet Ownership & Annual Expenses.) Cats are beloved, reviled and the inspiration for much philosophy, the focus of humor (see The Quote Garden, Quotations about Cats), and endlessly interesting to some people -- a Google search for "cat videos" produces 352 million results.
Cats bite and scratch people. Liability generally is established by the so-called one bite rule. The basic rule, applicable to any animal including dogs and cats, is set forth in Restatement (Third) of the Law of Torts, section 23: "An owner or possessor of an animal that the owner or possessor knows or has reason to know has dangerous tendencies abnormal for the animal's category is subject to strict liability for physical harm caused by the animal if the harm ensues from that dangerous tendency." If a cat bites or scratches because it has a vicious temperament, the owner or harborer of the cat who knows about its vicioiusness is strictly liable for the injury and its consequences, such as pain and suffering, medical costs, lost wages because of inability to work, etc.
In some jurisdictions, there are strict liability ordinances that make a cat owner or harborer liable even if the cat never bit or scratched someone in the past. See, i.e., West Sacramento Municipal Code, section 6.16.210: "No owner of a domestic cat shall permit or suffer such cat to damage property, public or private or real or personal, or to bite, scratch or claw any human being or other animal which is the property of another." The violation of such an ordinance can also be regarded as negligence per se.