Hydrogen-producing assemblies, fuel cell systems including the same, methods of producing hydrogen gas, and methods of powering an energy-consuming device. Hydrogen-producing assemblies may include a monolithic body that defines at least a reforming conduit, in which a feed stream is catalyzed into a reformate gas stream containing hydrogen gas, and a burner conduit, in which a fuel-air stream is combusted. The monolithic body is constructed to conduct heat generated by the exothermic reaction of the combustion from the burner conduit to the reformer conduit. In some hydrogen-producing assemblies, the monolithic body further defines a vaporizer conduit, in which liquid portions of the feed stream are vaporized prior to being delivered to the reformer conduit. In such embodiments, the monolithic body is constructed to conduct heat from the burner conduit to the vaporizer conduit. Hydrogen-producing assemblies may be incorporated into a fuel cell system that is configured to power an energy-consuming device.