Yes and no.
Young Pets: young cats and dogs should start their vaccinations around 2 months of age. They receive a booster every 3-4 weeks until they are 4 months old. Their next booster occurs 1 year later.
Adult pets, never vaccinated: If your pet is older than 3 month of ago, and have not previously been vaccinated (or it has been many years, or you do not know their vaccination history), these pets should receive 2 vaccinations 3-4 weeks apart. and boostered 1 year later.
Once the above vaccinations have been given, some will require boosters each year (ie. Canine Cough (Bordetella), Leptospirosis, Lyme disease, Feline Rabies, Feline Leukemia). Where as other vaccinations will only require boostering every 3 years (ie. Parvovirus, Distemper, Adenovirus, Canine Rabies, rhinotracheitis, calicivirus and panleukopenia). Ideally, these 3 year vaccinations are introduced individually, and rotated over 3 years to minimize amount of vaccine product given at any single time.
Regardless of whether or not they are due for a vaccination, each pet should have a complete physical examination each year as we cannot rely on them to tell us when something is not quite right.