Police is always paid, no volunteers there.
Paramedics are often paid ("Regelrettungsdienst"), but there are lots of units working on voluntary basis which take care of festivals, larger events and more and are somewhat on stand-by in case the Regelrettungsdienst gets overwhelmed with work.
Firefighters are the most and they are almost always volunteers, the so called "Freiwillige Feuerwehr". As a member of the Freiwillige Feuerwehr you'll have some kind of pager or app to alarm you and people will then leave work and rush to the fire department and man the trucks. Only large cities (> 100k residents, I think) need to have paid firefighters.
Firefighters and Paramedics are also among the jobs with the highest trust/respect with the people in Germany. (Sadly, attacks on those groups from bystanders are steadily climbing...)
These days thousands of people have left their work (your city will pay your employer for the time you had to leave, although most employers don't bill that time) to help take care of the aftermath of the floods, either as Paramedics or Firefighters.
Usually there's no compensation for this work, next to getting something to eat and drink and the equipment.
This is probably quite unique compared to other countries.
Update: Seems like it's not unique to Germany. I appreciate that, thanks for letting me know.