Clearly vaccines have helped thousands of animals. Rabies for instance is fully preventable with vaccines.
I, in fact suggest that your dog or cat be vaccinated for rabies if they are at risk of contracting the disease.
But there is now some pretty powerful research suggesting that the rabies vaccine may give lifetime protection to your dog or cat (minimal 7 years), and should not be given yearly.
Overvaccination has been linked to a variety of adverse effects:
How vaccinations may affect your pet's overall health