99.9% of my dogs' diet is wholesome food. 0.1% is supplemented. I am a firm believer that the minerals and nutrients a dog needs should come from the actual food the dog is eating.
As the diet preparer, I know what I'm feeding and know what nutrients are in those foods. I try to feed all nutrients naturally before resorting to artificial supplements.
Websites like USDA and NutritionData make calculating nutrient intake amounts really simple and easy to utilize in your dog's diet (and your own!).
Deficiencies and nutrient excesses are also concerns. A full blood panel once or twice a year will provide excellent insight into your feeding and/or supplementation regimen.
Many supplements made for pet dogs and cats contain chemical preservatives and may not even have the listed amount of ingredients in the actual product. Here is a list of the recommended nutrient doses that should be in a supplement.
So what do I give my dogs? Shibas have a double coat, shed heavily twice a year and need support for skin and coat health. When they aren't eating whole prey, I give my dogs one fish oil capsule every other day. Intensive livestock practices find the farm animals that we eat being fed grain-based diets. As such, the meat that is produced is naturally low in omega-3. There is plenty of omega-6 in raw meat, but the balance of omega-3 to -6 is thrown out of whack. As a result, it may be necessary to supplement a raw diet with omega-3. Again, attempt to provide it naturally first. This can be done by feeding oily fish or grass-fed red meat. If you are unable to provide grass fed meat or fish in adequate amounts, then a supplement like fish oil capsules (human grade!) will suffice.
The absorption and utilization of omegas depends on the availability of vitamin E. It is possible to get omega supplements that have vitamin E included, if you can find something like that then it will be much more convenient.
Joint supplements typically include glucosamine and chondroitin. Before resorting to a bottled supplement, attempt to provide it naturally. Glucosamine is found naturally in raw joint tissue. So if you are able to feed edible bone "joints", then you are already providing natural glucosamine. Chicken feet are great, as are other joint items such as chicken or turkey legs, backs, necks, etc.
I also give my dogs (again, and myself) pre- and pro-biotics.