One of the greatest complaints most people have with training with food, or rewards of any kind, is that their dog will only perform when they have said treat or reward. It's a legitimate complaint because most people (and this would be the fault of their trainer) never learn how to fade the treat properly.
When we first are teaching a dog a new behavior or trick the fastest way to achieve proficiency and solid learning is with a continuous rate of reinforcement, they get a cookie every single time they respond correctly. So when we first teach our dogs to sit, every time they sit they get reinforcement, usually with food, as it's the quickest way to create a good association between the cue and the response.
However we then need to start requiring a little more from the dog. Perhaps we ask them to sit but only reward after a few seconds, which will help with stability in the position and not create a dog that pops his butt up immediately after sitting, this is called a Duration Schedule of reinforcement. Then when we have taught our dogs to have some duration in the position, perhaps we only reward the really fast responses, this is called Differential Reinforcement of Excellent behavior. Another way we could fade the treat is to require a certain number of behaviors to be performed before the reward is given, that is a Random Ratio or Variable Ratio.
Another way to fade the treat is to start substituting the food reward with some other reward such as petting, a game of fetch, tug or freedom off leash. I would venture to say off leash time is just as reinforcing, if not more for some dogs, as food is. Off leash time is a very powerful reinforcer. A classic example of this is sitting at the door to go for a walk; in the beginning we ask for a sit at the door, give a food reward and then walk out the door. But as your dog progresses you can start to expect more. Ask for the sit BEFORE you even leash him, this requires him to practice his sit duration while you attach the leash, then you can ask him to wait as you open the door and when he is successful the reward is going out for a nice walk or to play fetch in the yard.
What I see a lot of in class is this:
Owner: "Fluffy Sit"
Fluffy doesn't sit just stares blankly at owner (even though she has been thoroughly taught what sit is)
Owner "FLUFFY, SIT" (a little more loudly)
Fluffy continues to stand and stare
Owner reaches into their treat bag, pulls out a treat and says "SIT" and...Fluffy sits!!
A few things could be happening here;
1)The owner could have inadvertently taught fluffy that the cue for sit is actually reaching into her treat bag
2)The owner hasn't worked on proofing the behavior without treats yet, fading the treat
3)The dog is just being the opportunistic/intelligent creature it is and they have figured out that not responding brings out the treat! In essence Fluffy has trained her owner!
So the next time you ask your dog to sit and they refuse...walk away! See what happens then; if they follow you, ask them to sit again. If they respond give them verbal praise and petting or play a game of tug. Continuing to require "more" from your dog and refusing to resort to bribes, for behaviors you know they have been taught, will go a long way in getting better response to your cues.