Food allergies are not common in cats -- in fact, are estimated to cause only up to 1% of all skin problems in cats, while other allergic reactions, such as to flea bites, are much more common. But food allergies can affect your cat's quality of life due to skin irritation and digestive problems such as vomiting or diarrhea. If your cat does show these symptoms, it's worthwhile to consider food allergies as a potential cause.
Some cats are allergic to certain proteins in beef, eggs or wheat, which can lead to itching or diarrhea. By contrast, cats that get diarrhea after drinking milk are less likely to have an allergy than simply be experiencing something many humans know all too well: lactose intolerance.
Your vet is the best source to determine whether your cat has a food allergy, another type of allergy, or is getting sick from something else entirely. If a food allergy is the primary suspect, your vet may prescribe an "elimination diet." Elimination diets can help diagnose food allergies by ruling out, one by one, the ingredients that commonly cause allergies. Once the allergy has been discovered, you can find a diet that is free of the allergy-causing ingredient.