When a cat is allergic to something, common indications will be itchy skin, coughing and/or sneezing, or vomiting or diarrhea in the case of a digestive allergy. Allergies to fleas, foods, things inhaled, or something they have come in contact with are the most likely allergies in cats.
Contact allergies generally result in a fairly localized reaction on the skin. The cat may scratch a lot or there may be an indication of irritation at the place of contact. Most common causes of contact allergies in cats would obviously be items with which they come in close contact such as flea collars, bedding, toys, etc. The simplest cure is to remove the contact.
Flea allergies are very common in cats. A normal cat may simply bite or scratch for a while and then go on to other things, but a cat with a flea allergy may scratch, chew, and worry at the spot until large amounts of fur are lost.
Inhalant types of allergies are probably the most common in cats. Your cat can be allergic to the exact same allergens that you are. Tree pollens, grass pollens, and weed pollens along with the rest of the items we humans fear; mold, mildew, dust mites, and dust itself can all trigger allergic reactions in cats.
As in humans, true food allergies in cats can be extremely difficult to pinpoint. One reason is that they commonly demonstrate many of the symptoms of distress seen in the other groups. True food allergies in cats can cause itching and/or respiratory problems. Most food allergies will center around the type of protein common in the cat's diet, such as beef, pork, poultry, or lamb. Simply eliminating that type of protein by changing to another type of food will usually take care of the problem.