Perhaps not measles, but I have heard this about the vaccinations for more serious diseases:
Approximately 1 in 100,000 children have a serious adverse reaction to the vaccine. Approximately 1 in 1,000 children have a serious adverse reaction to the disease.
As far as my child goes (went, actually; she's grown now), vaccination is the way to go. The 1 in 100,000 chance that she will have a problem pales before the fact that she will probably get the disease and, at the very least, be sick for a week or two (and at most, die).
Even the "vaccines cause autism" theory grows weaker and weaker now that thimoseral has been removed from all vaccines. It was used as a preservative and has been shown to cause problems, although the link to autism was never solidly proven.
Shewolf, can you tell me more about your aversion to keeping your child disease-free?