For cats and dogs the emphasis should be on meat.
For cats: Cats in particular are obligate carnivores, which means that they must get their nutrition from meat (dogs' diets can be a bit more varied). Freeze-dried meat, organ meat, poultry, and fish are great options; the ingredient listing on the package should be simply 100 percent tripe, salmon, or whatever the protein source. Rawhide can cause digestive upset and often contains harsh chemicals.
For dogs: Better dog chew treats include dried beef tendons, beef trachea, and "bully sticks." Biscuits can be another occasional option for dogs, but make sure that they are small and don't contain wheat or corn. Carbs less likely to cause allergies and other problems include potato, sweet potato, and tapioca.
From your kitchen: Your fridge and pantry also offer choices, but it's important to know that there are foods that pets should never eat, such as anything containing the artificial sweetener xylitol or more than trace amounts of garlic and onions. Grapes, raisins, chocolate, and macadamia nuts are unsafe for dogs. You can give your pet a little piece of cheese or cooked meat, or some peanut butter. Some dogs enjoy raw or cooked vegetables, such as carrots, broccoli, and sugar snap peas. An oil- or water-packed sardine fillet makes a nice kitty delicacy -- guaranteed to elicit purrs.