Right, but there are a lot of federal agencies that adjudicate and potentially give out harsh fines without actually being a court. If you are in that situation you do not have the right to a jury trial, at least until this case was decided.
That's not true for all civil cases, though. The Seventh Amendment says, "In suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, ..." As has been described elsewhere here, this was interpreted to provide a jury right in suits at law but not in equity. You can also waive your jury right by agreeing not to invoke it, say in a contract.
> Under Penal Code sections 17(d) and 19.8, if certain offenses are charged as an infraction instead of as a misdemeanor, you can ask that the infraction charge be tried with a jury as a misdemeanor.