Yep, I'm one of "those" parents. I don't believe that my children need more than three times the number of vaccinations than I had just 30 years ago. I don't believe that diseases have grown so exponentially that I need to inoculate my kids out the wazoo. However, I DO believe that they need some vaccines and I've never understood the "don't ever vaccinate" camps rhetoric. Polio, measles, mumps, etc... are real and our kids have access to medicine that prevents those diseases....as should every child on the planet, but that's a different article.
So, here's one of the best articles I've ever found that gives a real view of BOTH sides, and presents us with realistic measures that can be put in place. It's actually a post about the movie, "The Greater Good". I'd suggest watching it, but if you don't have time, please read the article. It's awesome!