The choice to feed dairy to your dog is an individual one. I have been told and seen published that dogs should never ever ever (how dare you even consider it!) be fed dairy products. But why? It causes diarrhea. How?
Dogs can be, but are not necessarily, lactose intolerant. This means they don't produce the enzyme required to break down lactose just as some people don't.
The most important thing to consider when feeding a dog a dairy product is its lactose content. Some dairy products have significantly less lactose than others. Yogurt has about 1/3rd of the lactose that whole milk does.
Some dogs have some level of lactose intolerance. Therefore, careful consideration to the form of dairy you choose to feed should be given. Sharp cheddar cheese has basically no lactose. Sour cream and cottage cheese both have less lactose than yogurt, but a little more than that of a good hard sharp cheese. Too much lactose is where the diarrhea comes from in dogs who don't tolerate it well.
The next consideration should probably be why you're feeding dairy products. Yogurt is a great source of live, active cultures and probiotics that are fantastic for your dog's digestive system. Like us, your dog can benefit greatly from a boost to the helpful gut bacteria that aid them in digestion and in keeping bad bacteria in check. Yogurt is a very good option if you've got a dog who is exceptionally gassy. (Let me just tell you about my girl who loves to fart, watch us all open the windows, stick her head out and take a deep breath. Then, when we roll the windows back up, fart again...)
Feeding other low lactose cheeses or dairy products like cottage cheese can provide lots of calcium, protein, and plenty of fat for your dog if he or she is in need of any of these things. Growing puppies sure benefit from all of the above! Cheese is also a yummy way to hide medications or to use as treats when training.
Lastly, I'm sure you're wondering how much to feed. It doesn't take much. A heaping tablespoon of plain yogurt per day is enough to feed for assisting in maintaining a healthy digestive system. More can be given if you're dog is on antibiotics which are notorious for killing off the good bacteria in the body that keeps things moving along.