This isn't technically a history question, as 'cavemen' (more accurately, later paleolithic humans) existed before written records, so it would properly fall into the field of prehistory or anthropology in general, but I can still give you an answer.
Yes, they did get dental caries (cavities), but at a fairly low rate, and generally later in life. The development of agriculture is what really created tooth decay as a problem, with rates increasing by about six times overall, and for the first time becoming an issue with children. This is because the bacteria that cause tooth decay feed on sugars and other carbohydrates, which have a much higher prevalence in agricultural diets than otherwise. This issue has of course continued through the twenty-first century, where it remains prevalent among agricultural societies, but at least we know there's a simple solution- just ditch grains and processed sugar and subsist on meat and vegetables, and you probably won't need to brush your teeth again (though don't quote me on that to your dentist!)