When you require treatment for something more than the common cavity, it usually requires that you see a dental specialist. Ideally, your dentist can recommend good specialists, but if need be, call your local university's graduate dental school for references.
Here's a run down of the oral health specialists that are out there:
If you have areas in your mouth that show symptoms of the supporting structure of the teeth - gum and bone - breaking down, your dentist will send you to a periodontist. This specialist examines, diagnoses and treats the manifestations of gum problems. He'll eliminate the pockets, perform bone or tissue grafting, place implants, and meet any of the whole host of requirements necessary to heal any problems with the supporting structure of the teeth.
The prosthodontist is specially trained in aesthetics and function of the mouth. If you're contemplating restorative dentistry, changing old fillings, sensitivities in the mouth, the super-restorative dentist is the prosthodontist, specially trained in the form and the function of teeth and, specifically in restoring them. A prosthodontist is a dentist who went for post-graduate training in these areas.
(Note: A general dentist can also be an excellent restorative dentist with the proper training.)
An endodontist is specially trained in diagnosing and treating problems associated with the inside of the tooth. If you need to have a root canal, it should be done by an endodontist.
An orthodontist examines, diagnoses and treats irregularities of tooth position and malrelations of jaws. If you or your child needs braces, you should see an orthodontist.
The Oral Surgeon:
The oral surgeon takes care of any surgical needs. Under this umbrella are biopsies, and removing anything pathological in the mouth, including wisdom teeth. He is also trained to place implants, so you can choose between the oral surgeon and the periodontist for those.