Just like people, pets can have food allergies. For dogs the most common food allergens are chicken, beef, dairy products, pork, wheat, corn and eggs. A less common but recognized food allergen is rice. Notice that all of these items are the most common ingredients in pet foods…Notice also that we are dealing with proteins (meats, etc) most of the time, not grains.  Grain free foods are not the answer, but pet food companies do a good job of advertising that they are.

What are the signs of food allergy or adverse food reaction?
The most common sign of food allergy or adverse food reaction is year-round itching. Dogs with AFR often rub their face/ears, lick their feet, and often "scoot" on their bum. The itch can be everywhere (generalized.) Ear and skin infections are common. Some food allergy pets have just recurrent skin infections (pyoderma) or just ear problems. Cats often have intense scratching and crusting on the head and neck, and they may lick the hair off their belly.
The signs of food allergy usually develop by 3 years of age. Some pets develop AFR as young as 4-6 months of age. Food allergies start after eating the offending food allergen for some time, not because a pet's diet has recently been changed.
How are food allergies diagnosed?
A period of diet restriction or a food trial is necessary and the ONLY way to determine if a pet has AFR. There are blood tests available for food allergies, but there can be false positive and false negative results on these tests. Until these tests are improved, the only way to know if a pet has food allergy is the hard way: diet restriction. 
What's involved in diet restriction?
We use several types of restricted diets. The first type is a home cooked diet consisting of a protein and carbohydrate source the pet has not eaten. The next type is a commercial prescription diet that contains a protein and carbohydrate source the pet has not eaten, such as Royal Canin or Natural Balance duck and potato, or Iams fish and potato. The other type contains hydrolyzed ingredients: the protein is enzymatically broken into smaller blocks of amino acids as the food is made. In theory, the protein size is too small to be recognized by the immune system and therefore cannot trigger the allergy. Examples of this type of diet are Hill's z/d ultra, Royal Canin HP and Purina's HA. Sometimes we recommend home-cooking, the best food trial.
The MOST IMPORTANT (and most difficult) part of a food trial is restricting what your pet eats to this food ONLY. This means all other treats, snacks, supplements, rawhide, pig ears, flavored chews, greenies, bones and even flavored medications such as Rimadyl and heartworm preventive MUST be stopped during the food trial (unflavored versions of those two medications are available.) Even one small bite of cheese, bread, pizza crust, sandwich meat, etc., can trigger the allergy and negate the food trial. It is also necessary to treat any infections the pet has when we start the food trial; infection itself makes the skin itchy! If infection keeps the itch going, we could falsely assume diet restriction did not help.
How long does it take to see results from diet restriction?
Some pets improve in 2-3 weeks; some take 2-3 months. Therefore, we recommend a minimum of 8 weeks on the restricted diet.
If my pet has food allergy, do I have to feed this special diet for the rest of their life?
Food allergies are a life-long condition, so pets have to avoid eating the things they are allergic to forever. However, we try to find a food they can tolerate that is less expensive than the prescribed foods and available in pet stores.