Last night during one of my group classes, I had a student raise her hand and ask "I don't know if it's too early to be asking this, but when can we stop giving them treats?". Since this is probably one of the most frequently asked questions I get, I discussed the answer with the entire class. And the answer is: it depends (of course!).
The fact of the matter is that treats are one of the easiest, most efficient ways to reward good behavior. If it was really important to you or your dog had some kind of allergy or food intolerance that you were sorting out, you could stop giving treats today as long as you were using SOME kind of reinforcer (i.e. fetch, tug, the opportunity to go outside or chase a squirrel). Remember, behavior that is not being reinforced will not continue to increase, no matter how hard you wish it would. HOWEVER. It would probably be detrimental to your progress due to the logistics of training without food reinforcers. Consider the following scenarios:
Scenario A: I'm teaching my dog to sit using his favorite toy, which we'll use to play fetch as a reinforcer. I can either lure using the toy (sometimes a challenge with a toy) or capture the sit, withholding the toy until the dog offers a "sit" automatically. After he sits, I say "yes!" and throw the toy for him 30-40 feet. He runs out to get the toy, returns to bring the toy, and we repeat this process (assuming this dog will willingly drop the toy, of course).
Scenario B: I'm teaching my dog to sit using tiny treats. I can either lure or capture the behavior. The dog sits, I say "yes!", feed him a treat, then step away or toss a "freebie" to reset him. Lather, rinse, repeat.
In scenario A, each repetition is probably taking at least a minute, if not more. The behavior is the same, but the time it takes the dog to run out, get the toy, and return it adds up quickly. In a five minute training session you're probably only getting in 5-10 repetitions of the behavior you are training for. In scenario B, you can efficiently and cleanly get repetition of the behavior with little to no time lapse in between, and may be able to get the same number of repetitions in a quarter of the time. Dog training is like any other sport: it involves muscle memory and repetition. The more repetitions you get, the more quickly that behavior will be learned. If we follow that rule, scenario B is FAR more effective than scenario A.
The other side of this question to me is: why do you want to stop using treats? During my time training and working with dogs I've found that some people think of using treats in training as a "crutch" or something that needs to be faded to prove that the dog is performing the behavior for you or out of respect, instead of for the treat. And this I say: Phooey! When my boyfriend is sick, I make him soup. When I made too many banana pancakes, I ran the extras over to my sister. When I make too many cookies I drop some off with my parents.
As a species, humans LOVE to use food to express their affection. Why does it have to be different with my dog?
Yes, I do teach my dog intermittent reinforcement (that is, he doesn't get a cookie EVERY time he performs a behavior) so that the behavior is more durable for "real life". I work with my dog when I don't have cookies visible on me so that he understands that visible food isn't actually part of the end behavior. I also use a variety of reinforcers (we use his favorite toy all the time to work on impulse control and manners). HOWEVER I also understand that everything my dog does is because he is either working for something he likes (COOKIES!) or to avoid something he doesn't like (the door closing if he breaks a "wait" before being released). Not because of "respect", "dominance", or any other vague idea that isn't even on his radar. So I say: let them eat cookies!