I felt like your comment was a good jumping off point for what I wanted to say. Every time an outbreak of a vaccine-preventable disease happens, anti-vaxxers cry out "but some of the infected people were vaccinated! So see, vaccines don't work that well after all!" (Not claiming you were saying this) But what they are missing are the rates of infection. Most people are vaccinated, and vaccines are usually effective somewhere above 95% of the time. So sure, you do have a small number of vaccinated people that end up infected. But compare infection rates in the following example:
Say 10,000 people visited Disneyland during the measles exposure period. The percentage of unvaccinated people in California is about 2%, so we can assume about 200 people there were unvaccinated. So say 10 people wind up with measles; 5 were vaccinated and 5 weren't. Someone might look at this and think "hey, it's the same number on both sides. WTF vaccines?!" But when you look at infection rates, you can 5/200 or a 0.025% infection rate for unvaccinated people who were at the park during that period, and 5/9,800 or 0.00051% of vaccinated people there who got sick. That's a magnitude difference of 50. 50!!!
A fun fact about measles is that without heard immunity, the infection rate is 90%. It's one of the most contagious diseases there is. As heard immunity breaks down due to lack of vaccination, the rate of measles will grow exponentially. Which sucks pretty badly for those of us being responsible and getting our shots.