The two replies above are both true and important. I'm going to add a few more important points:
1) A whole bunch of diseases don't have vaccines for children under, say, 1 year old. Other vaccines don't work very well on their first dose, so children aren't fully protected until they are a year old, or older. So these youngsters rely on the people who are old enough to vaccinate to protect them. This is why I don't let "vax-haters" come near my kids. Even if they think they are perfectly healthy, they could infect children.
2) Another common complaint: "It used to be that everyone just had chickenpox and mumps, so it's really no big deal." Some of the "vax-haters" will actually give their kids chicken pox and mumps, figuring "a minor case now beats getting really sick later" -- and to an extent, that's almost true -- if you get mumps as a grown-up, it really, really sucks. The problems are:
a) A small percentage of kids will get "really sick" now, and
b) Adults actually do get sick later even if they had a childhood infection.
Suffice it to say, the odds of getting really sick are vastly higher with these infection parties than ANY side effects of getting vaccinated.
Also, I would advise that you DO NOT google search images of extreme cases of these "mostly harmless" childhood diseases -- they're utterly horrifying.
Anyway, I've heard a lot of people say, "Results of vaccinations so good that people have forgotten how bad the diseases are, and therefore they argue about getting vaccinated."
I always liked Buffy, and now I have another reason to like Sarah-Michelle Geller!