Cats do experience a form of tickling called knismesis, which is the type that feels itchy or mildly irritating. However, cats do not experience the kind of laughter-inducing tickling that people do, which is known as gargalesis.
Knismesis is a common form of tickling that is experienced by a wide variety of animals, including both cats and humans. It is usually triggered by a light touch that may mimic the feeling of an insect crawling on the skin. This response has been widely studied in cats, and it may be why some cats suddenly attack the person petting them. Gargalesis, or heavy tickling, has only been observed in humans, rats and some primates.