Here's a history piece on the 1976 swine flu epidemic in which vaccines were developed and distributed throughout the U.S. And while swine flu did not break out into a pandemic, many people developed Guillain-Barré syndrome, a rare neurological condition that causes temporary muscle weakness or paralysis. More than 30 of those people died.
"Many experts say they do not think a vaccine for the new flu strain, called H1N1, would raise a similar risk for Guillain-Barré. But answering that question is difficult because to this day, no one has figured out why the 1976 vaccine caused the disease, in which the body’s immune system mistakenly attacks the nerves.
Indeed, some researchers still question whether the vaccine did cause Guillain-Barré, particularly since flu vaccines in other years have been linked to little or no risk of the disease."