Wouldn't it be a great world if our dogs could truly understand the spoken word; could learn just like babies do? 
I believe we talk far too much to our pets, expecting them to understand what we are saying and getting upset when they don't perform when we ask. That leads us to think they are stubborn or stupid or trying to take over the world with their "dominant" personality.

How about this option: they don't respond because they don't understand the meaning of the words you are using.
How arrogant of us to assume they "should" understand. We're speaking English, after all. 
The fact that they "get" as much as they do is amazing! One reason we assume they understand is because they sometimes do what we ask, often after much repeating and gesturing.
I see this frustration time and time again. People don't stop talking to their dogs. When I come into a house and begin training, I am pretty quiet. I avoid all excess chit chat and movement. People are surprised at how well their dog responds with so few words.
When I can get people to stop talking so much during the training process, and become aware of their body language, they are amazed at how quickly their dogs "get it". I point out their dogs are more often then not, tuning out their excessive chit chat and are instead watching their body language for cues, trying to figure out what's expected.

I put it to the test. Down is a good example. Most people insist the dog knows how to do it. I ask the client to cue "down" using the word only once,not repeating it and standing perfectly still. Most dogs just stare up, waiting. Then, I ask, cue "down" using their usual hand signal, no words. Success!! 
Many dogs spend more time watching following your unintentional body movements, than following your words. I have noticed, the more chit chat, the more the dog watches for cues from your body. 
Unless you have specifically and successfully taught the meaning of words (a doggie vocabulary), the dog likely is guessing or following your physical prompts. 

Think of travelling to a foreign country. The only language you have ever spoken is English. You are trying to get information but the person you are speaking to doesn't speak English. As you both try to find some common ground, the volume increases, gesturing increases, frustration increases. You might notice, as frustration with the language barrier increases, you are paying more attention to the gestures and less to the words. Perhaps you eventually have success. More likely, you both walk away, shaking your heads, frustrated because the person on the other side of the conversation couldn't figure out what you were saying. 

A great trainer, Kathy Sdao (www.kathysdao.com), talks about the importance of having a vocabulary for your dog. That includes making a list of all the words used, along with the precise meaning,as well as being careful of having cues that sound like each other (bow and down) or a single word used for more than one behaviour.
  "Down" is a good example of a word that is often given multiple meanings. I hear it used to mean "lie down" and "get off my body" and "get off the furniture". How confusing for the poor pup!
It is necessary to choose one meaning per word and stick to it. In my house "down" means lie down. If I want my dog to get off the couch,  I use "off". That means 4 paws on the floor.

I often suggest families sit down together and make a list of the words they use and what the expectation is for each word.

Too often we start using cues to elicit behaviour before the dog has learned the meaning of the word. This applies to any word you want the dog to know : come, sit, down, Rover, off, drop it, leave it; the list is endless.
When training my Beardie to respond to the word "come" (meaning run to me now), I made sure that I did not use it if I thought he would not comply. During training, I only said "come" when he was already running at me or if I knew 100% that he would (meal time). The other times, I whistled, wiggled a toy, ran the opposite way, did just about anything to get his attention - other that say "come". When he got to me I made sure he had an amazing reward. For him, the best reward was and still is play. 
When he was about 6 months old, I began saying "come" to elicit the behaviour as opposed to using it only if he was already running. I was very careful to make sure he would be successful.

I challenge people to stop talking so much. Be aware of how much you talk needlessly. Go about your day, keep your regular routine. Don't say anything as
 you walk towards the door or get your coat and boots. Does your dog still come to you expecting his walk?
Try the same thing for dinner. Just prepare his food, no words necessary.
See if he runs away while you prepare the bath or get out the brushes for grooming (unless he enjoys it and runs to you, in which case the same experiment applies!). 

The more you use a word and your dog doesn't respond, the more he learns the word has no meaning or value. If your dog is not responding to a cue, use that as information. He's telling you, "I don't understand" not "I am stubborn".