Use Good Judgement and Consult Your Vet
If you're not sure, just call your vet. There's a lot of info out there about what makes a healthy diet for animals. I'm going to avoid the raw/cooked debate here, but it should be noted that animal bones can splinter and cause internal injury. (Dog bones you can buy at the store are usually processed to make them safer, but it's always a good idea to supervise your dogs eating them.)
Raw food that is intentionally for animals may be a healthy option, but raw table scraps are more likely to contain bacteria or parasites and should be cooked but not seasoned before given as a treat.
What Not to Feed
Chocolate - Chocolate contains a chemical called theobromine that is toxic to dogs and cats but not humans. It can cause seizures and heart problems. Chocolate also contains some caffine.
Dairy - Our pets don't have much of an enzyme called lactase that allows for the digestion of dairy products such as milk, cheese, or ice cream. They could get indigestion, vomiting, and diarrhea from eating dairy.
Onions and Garlic - There are compounds in this family of vegetables that can cause GI upset and red blood cell damage in cats and dogs.
Grapes and Raisins - This one seems less researched so it's still unknown exactly why this happens, but this fruit can drop your dog's blood sugar and cause liver damage. There's less out there about cats being affected this way, but it's best to keep them away from grapes and raisins.
Xylitol - This artificial sweetener can cause liver failure in your pets.
Caffeine - Anything related to cacao seeds like coffee or chocolate contain compounds called methylxanthines that are highly toxic to dogs. Cats are highly sensitive to the caffine itself and can become very sick or have heart problems.
Alchohol - Animals just can't filter this as much as we can, and they can end up with liver and/or kidney failure pretty quickly.
Yeast Dough - If you haven't cooked your bread yet and you're tempted to give a bit to your pet - don't. It can expand and releases gasses in your pets digestive tract causing an emergency situation.
Citrus, Coconut, Coconut Oil - These can be ok in small amounts, but very irritating in large doses.
Nuts - Macadamias are toxic to dogs, and nuts in general are very difficult for cats and dogs to digest.
Avocado - Likely a bad idea for the same reason as nuts in that it's fatty and hard to digest. It is toxic to other animals like horses and birds.
Some fruits and vegetables can be ok to feed your pets, but in general avoid seeds.
There's some debate about raw eggs. Arguably they would be a part of your pet's diet in the "wild," but domesticated animals aren't always as hardy as their wild cousins like wolves or tigers, so they likely can't handle an egg with harmful bacteria. If you trust your egg source enough to eat them raw yourself they might be ok for your pet.