You don't need organic, you just need a high quality food. Science Diet is crap.
Not all pet food is made equally. A lot of it is full of corn, by-products, dyes, unhealthy preservatives, filler grains and all sorts of nasty stuff. A lot of pet food companies are perfectly happy to the dump cheap leftovers and things that aren't safe for human consumption (from human food processing plants) into their foods. Will it kill your dog? No, it has to be nutritionally complete and safe to even be marketed. Is it healthy? Not by a long shot.
Corn is a low quality ingredient you never want to see in your pet food. Corn and low quality grains are two of the biggest culprits when it comes to food allergies in our pets.
Thankfully, there are some excellent dog foods being made these days that include organic, human grade ingredients rather than trash not fit for human consumption.
Examples of low quality foods to avoid: Anything you can find in a grocery store will be low end, Purina, Iams, Eukanuba, Science Diet, Royal Canin, Pedigree, Kibbles n' Bits, Beneful, Ol'Roy.
Examples of high quality foods to look for: Innova, Wellness, Solid Gold, Canidae All Life Stages, Fromm Four Star, Merrick, GO Natural, Nature's Variety Prairie, Nature's Logic, Artemis Fresh Mix, Timberwolf Organics.
Although the high quality foods are more expensive, you're getting what you're paying for. Less filler material and higher quality ingredients means more concentrated nutrients... this means you typically need to feed far less of the high quality food than you would of the low quality one. Which also means less poop!
Seriously on a budget? Two of the most affordable of the higher quality foods would be Chicken Soup for the Dog Lover's Soul and Canidae All Life Stages.
Before following your vet's food recommendation, keep in mind that vets get /very/ little nutritional training during their schooling. Besides that, what training they /do/ get is usually sponsored or taught by... you guessed it, the crappy pet food companies! They also often get kickbacks from the companies for pushing these products at their clinics (Science Diet, Royal Canin etc.)
A great option is to go with an entirely grain-free diet. Many of the high quality foods now put out grain-free formulas. Some good grain-free diets include: Innova EVO, Wellness CORE, Blue Wilderness, Nature's Variety Instinct, Orijen, Horizon Legacy, Canidae Grain Free All Life Stages, Fromm Surf & Turf, Now!, GO Natural Grain Free, Sold Gold Barking At The Moon, Ziwipeak, and Taste of the Wild.
Some pretty decent foods can even be found in common pet stores. Petsmart carries Blue Buffalo products (such as the excellent grain-free diet, Blue Wilderness). Petco carries Wellness, Solid Gold, Natural Balance, Eagle Pack Holistic Select, Blue Buffalo, Castor & Pollux Organix, Pinnacle, and Halo.
If you can't find a food, most of the high quality dog food brands have websites with store locators on them that will help you find the store closest to you which supplies their products. Simply type the dog food brand's name into Google, go to their website, and type your zip code into their store locator.
Another option, if you can't find anywhere around you that sells good foods, is to order your pet food online. Here's an excellent place to do so: http://www.petfooddirect.com/store/
Remember that foods should be switched gradually (mixing the new slowly in with the old over the period of about week or so), especially when switching to a higher quality one, so as not to upset tummies. For example:
Days 1 & 2: 75% old food, 25% new food
Days 3 & 4: 50% old food, 50% new food
Days 5 & 6: 25% old food, 75% new food
Day 7: 0% old food, 100% new food
Another option for feeding dogs is to feed raw. This is something that should be thoroughly researched before being attempted:
http://www.rawfed.com/ (RawFed)
http://www.rawlearning.com/ (Jane Anderson's Raw Learning Site)
http://rawfeddogs.net/ (Raw Fed Dogs)
http://www.rawmeatybones.com/ (Raw Meaty Bones)
http://rawfed.com/myths/preymodel.html (Raw Prey Model Diet Vs. BARF Diet)
http://community.livejournal.com/rawdogs/profile/ (Raw Dogs Livejournal Community, excellent raw feeding information on the profile page and overall helpful community for raw feeding questions)
http://www.rawfed.com/myths/index.html (Myths About Raw Feeding)
Also remember that freefeeding (leaving food down) is the fast lane to canine obesity. Make sure to have scheduled feeding times loosely based on the feeding guidelines on your dog's food. Adult dogs are typically fed two meals a day.
More on dog food:
http://www.dogfoodproject.com/index.php?page=main (Learn how to determine the quality of your dog's food.)
http://www.dogfoodanalysis.com/dog_food_reviews/ (Dog food reviews. Four stars is a decent food, five stars is a great food, and six stars is an excellent food.)
Edit: LOL Salt&Pepper. That's a good one. Yup, a food made up primarily of corn is /totally/ equal to a food made up primarily of meat proteins. Thanks for the laugh!
Darksong~