First, no vaccine is 100% effective. You can be vaccinated for something, yet still get the disease if you're exposed consistently, or with a great intensity. Thus, the goal of most vaccinations is to achieve "herd immunity", wherein enough people within a population are vaccinated that the chance of any person being exposed to a case of the disease is low enough that even an imperfect vaccine can be considered 100% effective.

If herd immunity is not achieved, then even the best vaccines will fail to protect some percentage of the population. Outbreaks will occur, and vaccinated people will succumb; in particular, people with weakened immune systems, the elderly, and pregnant women are susceptible to diseases, even when vaccinated.

Second, for some diseases -- such as chickenpox and rubella -- incomplete immunization of a population actually results in worse epidemics, because the incomplete immunization of a population tends to shift the cases of the disease to older people. And for diseases like chickenpox and rubella, childhood infection is relatively innocuous, whereas infection as an adult can kill you.

This latter concern isn't merely hypothetical -- there was a recent example of the consequences of incomplete vaccination in Greece, in the early 1990s. Because the Greeks had only inconsistently vaccinated for rubella starting in the 60s, there was a huge outbreak of adult rubella infections in 1993, and as a result of that, there was an epidemic of rubella-related spontaneous abortions and birth defects (a condition known as congential rubella syndrome, which is a hideous disease that the rubella vaccine was arguably intended to prevent). Had the immunization rate for rubella been high enough to achieve herd immunity, this never would have happened.