The Centers for Disease Control and Prevention (CDC) is a national public health institute in the United States. It is a United States federal agency, under the Department of Health and Human Services, and is headquartered in Atlanta, Georgia. (Wikipedia).
The CDC has a page outlining historical vaccine safety concerns. It concludes that the benefits of vaccines easily outweigh the risks. Ten incidents of concern since 1955 are listed on the page, and the conclusions provided.