Obviously we don't have precedent for mRNA vaccines like the now available SARS-CoV-2 vaccine from German-American Joint Venture Biontech/Pfizer.

But how about the other, more conventional vaccine technologies? Was there at some point ever a trial which needed to be suspended because e.g. after 3 years people, which initially (first few months after being administered a vaccine) seemed totally fine, got health issues?

This seems to be the crucial question, as we already vaccinated a large group of people, but were not able to observe them for very long.