This is perhaps the most important question regarding the health of our animals, because health begins with diet. If you're feeding Science Diet because your Vet has prescribed it, you may want to question what kind of a Vet you are using. Read the ingredients: cats and dogs did not evolve to eat corn and soy! The Vet who prescribes Science Diet is padding their income with sales of an inferior pet food product, and in my eyes, this is unacceptable.
Your dog's dream dinner
This is not to say that I haven't fed my dogs commercial kibble. It's just that I've noticed such a huge difference in their overall health when I'm feeding raw and homemade foods as compared to kibble, that it's definitely worth the time and investment, in my opinion.
The best way to tell if your dog is thriving on their diet is to look at their stools: they should be solid, and while they will smell, they shouldn't smell like toxic waste. If your dog is having consistently loose stools you will probably see anal gland problems as well. When my dogs are eating raw, their stools are very small and hard, hardly have any smell, and they never have anal gland issues. The stool will dry up into a white powder, because basically all that's left behind is the calcium from the chicken bone. You will find, with a kibble that is full of un-digestible junk, a larger than normal amount of waste coming out the other end. This is due to the corn and soy and other ingredients that your dog really doesn't want or need in their diet.
Another indication that you've found the right diet is a healthy, shiny coat, free of dandruff and hot spots. Their ears should also be clear and odor-free. Basically, you will see the usual indications of good health, and if your dog's health is not where it should be, look to the diet as the first change.
If you are interested in a list of quality raw commercial foods check out this site: Dog Food Advisor. If you are interested in preparing home-cooked or raw food diets for your dogs, this takes some time to research. Here is a good place to start: Dog Aware. This is also a good website to check out: Dog Dish Diet. The best site for ordering raw food that I've found so far and absolutely love is ReelRaw. I also supplement with food from Honest Kitchen (steamed and dehydrated whole foods) and I and Love and You (freeze dried raw). I also feed them a couple tablespoons of coconut oil every day and often give them turmeric with a little bit of honey.
In the past, I have fed my dogs Nature's Variety Instinct raw patties and was very happy with the results. I haven't personally tried but have had very good feedback on Stella and Chewy's. Another good place to look for raw food for your dog is at your local butcher or farmer's market. Some local farmers actually make raw dog food, but at the very least, could provide you with the ingredients. If you are uncomfortable feeding whole bones, you could always get a commercial meat grinder. Please make sure if you feed raw, that you do the proper research and add in an appropriate veggie mix, organ meats, and plenty of probiotics. Also, you MUST THAW raw bones before feeding, because frozen raw bones can splinter much like cooked bones.
My cat is not as keen on raw and homemade foods, so I feed her a diet that consists mainly of canned food. My favorite canned food to feed her is B.F.F. (Best Feline Food). I've only been able to find this online and in specialty pet stores, so I also have some grocery store options if you are on a budget or can't make the special trip to a boutique pet store. My cat loves Newman's Own Organics, and to save even more money, I buy the canned dog food. If your cat has a sensitivity to grains, they make a grain free cat food. Another grocery store brand my cat finds acceptable is Variety Homestyle Recipes. Again, you can buy the dog version and save a lot of money, but the cat version is grain free. As far as the protein content, they are about the same. Remember, feeding your cat canned food better replicates their natural diet. I know you might be concerned about having it ruin their teeth, but my cat is 11 years old, and I've only had to have her teeth cleaned a couple of times in the past 9 years that I've had her.
My dogs, on the other hand, are both seven years old and I've never had to have their teeth cleaned... I don't brush them either. Do wolves own toothbrushes? No. Neither do my dogs! Please let me know if you have any specific questions about feeding raw, I'm happy to share my personal experiences with you. There's just so much information and so many great resources I could go on for days. Hopefully this article will get you pointed in the right direction...