Are there any dangers to getting too many fillings?

No: The danger is leaving cavities to further degrade your teeth and lead to tooth aches and infections.

No: Fillings are repairs to damaged tooth structure. You run the risk for more harm by not having the teeth repaired. If you have numerous fillings that need to be done you may wish to reconsider your dietary habits, hygiene habits and consider visditng the dentist more not less.

Not usually: There are many different kinds of fillings. Once you've saved your teeth with all of these fillings you have to have a dentist keep an eye on them to make sure you don't get new cavities. Silver mercury fillings can eventually cause small cracks that can break your teeth. White fillings are more technique sensitive and have to be done perfectly or else they'll get new cavities.