Is there a specific reason that you need to brush the dog's teeth?
If a dog is eating standard dog food only, then there really is very little, if any, need at all. I'm sure it does happen but I've never personally known a dog to suffer dental issues. Probably because they don't subject their teeth to the sugary foods that we do.
Actually I've been told by the vets, and by doggie daycare staff, and also read in several books and websites on dog care, that it is a good idea to brush your pet's teeth regularly. They recommend once a day! I admit I'm not that good...! they say it's because dogs' teeth, like ours, can build up plaque and bacteria can accumulate and lead to gum disease later in life. Not to mention bad breath. I do know quite a few other dog owners who do brush their dogs' teeth at least occasionally. But I know it sounds strange.
Dogs do naturally clean their teeth when they chew on hard things like bones or hard chew toys. But is it "enough"? I don't know, but to err on the side of caution I don't think so...drawing on my own experience only, I know that all my previous dogs had typical "doggie breath" and I never brushed their teeth because I didn't know to do so. I thought doggie breath was just natural and inevitable, like doggie drooling. But my present dog does not have bad breath, his breath is odorless, even though he occasionally eats yucky stuff he finds on the ground (after which I definitely brush his teeth as I don't want him kissing me then, eek!!), and I regularly brush his teeth. at his recent annual checkup the vet said his teeth and gums were in excellent health. But when I pet some other people's dogs, I often see yellow teeth or smell offensive doggie breath. So maybe regular teeth brushing does help after all. Also, dogs have a biological urge to chew throughout their lives, so I imagine that developing tooth or gum disease that would make chewing painful has got to be really horrible for them, so I think it's better to take precautions anyway.
I also think that for modern domestic dogs who live in such close quarters with us, sharing our furniture or maybe even sleeping in the same bed as us, calls for increased standards of hygiene compared to dogs of previous generations who may not have spent so much time in such close quarters indoors with us.
I think that wild dogs or wolves probably chew on more hard substances than the typical modern pet dog, either that or they do in fact develop oral diseases later in life and maybe that is one of the things that kills them as part of natural selection. (Or maybe in the wild they tend to die from other causes long before oral disease sets in...)
It is also recommended that when your dog is 5 years old or so, that you take him to the vet for a full teeth-cleaning, but as this is where they put the dog under general anesthesia, it is a a rather big medical event.
By the way an easy way to brush your dog's teeth without actually putting your hands in his mouth, is to just smear the doggie toothpaste on his hard chew toys. they make some chew toys that are specifically designed for this, they have nubs or bristle-like protrusions in them that "scrub" the dog's teeth when he chews them. you can check the petstore for these, they are usually in the grooming section.