It's no big deal when a dog skips a few meals but this can cause a serious problem for cats. Cats that don't eat for a day or two can develop a life threatening condition called hepatic lipidosis, or fatty liver disease in which fat deposits move into the liver and clog up cells.
Symptoms include a swollen abdomen, loss of appetite and yellowish eyes and ears - signs that bile is accumulating in the body. See your vet immediately if your pet has these symptoms.
If your cat is not eating, check with your vet to find out why - don't let it go for days.