We humans grow two sets of teeth in our lifetimes. The first, as small children, are very small, but help us to eat solid food. Then, as adolescents, the first set falls out and are replaced with the larger set of teeth that we have as adults, and these are meant to last for our entire lifetime. We also, in our mid-twenties, grow a third set of molars, the so-called "wisdom teeth," because you're supposed to be wise by the time you get them.
Unfortunately, our teeth don't always last a lifetime. Sometimes people lose them due to trauma, as a blow to their face damages their teeth sufficiently to make some of them fall out. Others lose teeth to neglect, as tooth decay rots them until they fall out. Dentists have a few material options to replace lost teeth, from increasingly realistic-looking ceramic implants to dentures in extreme cases.
However, these are not the only options. Sharks are very hard on their teeth, and as a result, are constantly losing them. Like an adolescent human, a shark's teeth are constantly falling out and being replaced with new ones. Unlike an adolescent human, this process in sharks never stops.
I doubt we'll be able to have ever-regenerating teeth in the near future. However, I do see it as possible to extract a small piece of bone, and encourage it to grow into a tooth-like shape, which can subsequently be implanted, as a damaged tooth that fell out can often be re-implanted if preserved well enough. The bone-section should be grown in an intracellular-medium-like substance, and should be supplemented with adult stem cells, taken at the same time as the bone section. They should be fed with glucose and calcium, and the tank kept sterile. (Sugar alone doesn't rot your teeth, it's sugar plus mouth bacteria that are harmful.)