I work in a dental office that doesn't accept HMO's and happy to share my thoughts on this.
Background Info: most HMO plans pay dentists a certain amount for each contracted patient/month (let's say $10/month). Dentists receive this money for each patient whether or not they perform any procedures for this patient. If a dentist has 1000 HMO patients, then they receive a check for $10,000/month from the insurance company. Basic preventative services (cleanings, exams, etc) are covered by the HMO. If a patient needs restorative services (fillings, crowns, bridges) then the dentist is required to see them and the patient pays a low co-pay for the service (far less than a PPO plan).
Pros: Some dentists love this because it is guaranteed income whether or not you see the patients. In theory, the plans incentivize better preventive care (which is cheaper than expensive restorative procedures).
Cons: Dentists receive far lower reimbursement rates for the same services. Many of the patients who have cheaper HMO plans need a lot of dental work. The combination of these factors causes HMO patients to be under treated. I saw a patient yesterday who was on an HMO plan for years and her dentist told her that her teeth were great. When she finally went to get a second opinion she needed fillings on over 20 teeth. This is an extreme example but can happen under an HMO plan.
Reality Check: If you are a young dentist starting your own private practice you will probably take any patient/patient's insurance that you get. You probably will not have the luxury of choosing to not accept HMO plans. As more and more companies want to cut costs of employee benefits there will be more patients with HMO plans.