I have noticed that some people seem upset if I allow my dog to sniff their dog. I have seen some owners actually discipline their dog for sniffing another dog. Is there a rule to this?

Dogs sniff each other when the first meet as a way of checking each other out. There is nothing wrong with a dog sniffing another dog and I personally prefer it as I believe it helps with their socialization.

Some people may be against this for whatever reason (their dog might be aggressive, they may want their dog paying attention to them instead of the other dog, etc.)

My dog likes to be dominant over other dogs, so I watch him carefully when he interacts with another dog. Because he's more dominant at home and in the neighborhood than he is at the dog park, I'll keep him on a leash while at home. That way, if I begin to see a sign that he may be getting uncomfortable, it's easier for me to take him away. If he sniffs the other dog and doesn't react domineering, I'll reward him with a treat (trying to condition him.)

Sorry for the rambling. In a nut shell, the only rule I believe in as far as letting dogs sniff each other is you have to pay attention to your dogs body language and behavior.